TLDR:Yes,there is,but bad news: there's a lot of it and hence I can only go through the most famous accounts and they kinda sorta understood it but kinda hated it.

Well,the answer is incredibly complicated,spreading across some 3-4 centuries of missionary work (depending on the country). For my answer,I'll keep it within the field of my reading ie the early missionary period of China and Japan (Sorry,rest of Asia! and I hope someone else can come and answer queries on further periods and regions)

In the case of China,missionary activity started fairly early,with the arrival of Matteo Ricci,an Italian Jesuit who lived in China from 1582 to his death in 1610,easily the most famous figure in Chinese Jesuit history.He made a world map for the Wanli emperor,translated Euclid's works to Mandarin and much more.Most importantly,he wrote one of the earliest works on China to a European audience the De Christiana expeditione apud Sinas which was published after his death. It's a behemoth of a work,spanning 700 pages and talks about everything Matteo experienced in China from its customs to its economy,to its military and,of course,to its religion.

So what did Matteo Ricci think of the 3 major religions of China ie Confucianism,Taoism and Buddhism ? Well,on Taoism and Buddhism,he hated them with a passion.He felt that they were religions too obviously incompatible with Christianity and sought to communicate them as awkward versions of Christianity. He refers to Chinese Mahayana Buddhism as Sciequia or Omitose (bastardizations of Shakyamuni and Amitabha respectively). He stressed its mythical origin in the book (ie after Emperor Ming of Han received a prophetic dream about Buddhism in 65AD) and believed that Chinese Buddhism was severely influenced by Western thinking.He wrote that "the Buddhist concept of transmigration of souls is similar to that of Pythagoras in the West and even the Chinese five elements are nothing but a "foolish" extension to that of the western Four elements."He further compared the similarities between Buddhist chanting and Gregorian chanting,ecclesiastical statuary and vestments and the existence of monastic lifestyles to the Chinese appreciation of celibacy and the idea of "karma" in the east with the idea of virtue in the west,coupled with reward and punishment in the netherworld being a common tangent in both cultures. Eventually,he concluded that Buddhism had a "holy trinity" but does not talk any more of this so the exact components of this pantheon are unknown although Siddharta Gaudama ("Buddha") and Avalokiteśvara (Guan Yin) would likely be in. Ricci attributes all these similarities to Christianity to St Bartholomew the Apostle of the bible whose message the Chinese had somehow corrupted and/or forgotten.

On Taoism or Tausu as he calls it,Ricci dosen't appear to either know too much about it or didn't bother to write much about it.He mentioned the "Three Pure ones" or 三清 in Taoist mythology and conflated it with a "Buddhist trinity" but acknowledged them as "the father of lies" preserving at "his ambitious desire of divine similitude" ie Satan performing false idolatry.He gave an example of the "present reigning lord of heaven" Ciam who usurped his position from a previous lord (Liu) and mentions "those who have been taken bodily into heaven),further referencing Satanic themes.Confucianism was amenable to Ricci,however, in his writings.There is a notable lack of disparagement of Confucianist practices and,indeed,he was criticized by later missionary rivals such as the Dominicans, Franciscans, and Augustinians for being too "lax" on it.In his mind,Confucianism was a moral philosophy which only guided moral actions and not spiritual affairs.Hence,in his eyes,it was able to exist with Christianity.He would also go on to write The True Meaning of the Lord of Heaven, a book written in Chinese to try and convert the native Chinese into Catholicism. This was not a universally held view,however,as the Great Rites Controversy would later prove.However,in terms of early missionary work, Ricci sets the tone for European impressions on China.But wait,you ask,there's a 4th religion ! What about the hodgepodge rituals of the Chinese Folk religion ? Well Ricci treated it with disdain.He criticized Chinese alchemy,fortune-telling, palmistry, astrology, and geomancy as "absurd superstitions" and felt that the "addiction" to alchemy was both backward and superstitious.In fact,he writes about this as an anecdote :He was originally approached by the gentry so as to teach them the secrets of turning mercury to silver!

All in all,the early Jesuit ideas were that Buddhism and Taoism were simply corrupted ideals of Christianity proliferated by false priests ( Osciami he calls them but they were actually Buddhist monks). The question is Why. Why did Matteo Ricci not outright call them heathens (he did) with a false religion (He didn't). It is important to understand the context on which this is written.Matteo Ricci was the first Jesuit to seriously attempt to understand Chinese customs and language and he was ,hence,also the first to be treated seriously by the Chinese.Despite his acclaim as a court scientist in the Wanli emperor's court,it was unlikely that he forgot that he was,first and foremost,a missionary.A likely reason for this is that while Matteo was in his 30s when he went to China,he was nearing 50 when he truly achieved some headway by being summoned to the court of the Wanli Emperor. It was likely(at least in the view of Gallagher) that his hidden message for Sinas was for the Jesuits to continue his work by not giving up and encouraging them that China was not a lost cause.

But hold up,what about Japan ?! Luckily,there are first hand accounts of Japanese religion as well! Look no further than Francis Xavier's works to have an initial impression of Jesuit missionaries on Buddhism. Xavier's most famous account of Buddhism is a letter dated January 29th 1552,Xavier rightly noted that Buddhism came to Japan by way of China and describes the mortality of Buddha,specifically "Xaca [Śākyamuni] and Ameda [Amitābha].” .He further mentions the “nine principal sects” of Japanese Buddhism, by which he appears to have meant Tendai, Shingon, Nichiren, the Zen schools of Rinzai and Sōtō, and the Pure Land traditions of Jōdo-shū, Jōdo-Shinshū, Ji-shū, and Yūzū-Nembutsu. He disparaged all of them,saying that all of the 9 "recognized heaven and hell in a confused manner" while mentioning that the 5 principal prohibitions of Buddhism had 250 rules for monks and 348 rules for nuns,satirically calling them the "three hundred and five commandments” .However,he noted that whatever their rivalries or doctrinal differences, all nine sects saw in their founder a man who had shown "compassion for his followers and performed great penances on their behalf."Xavier certainly understood Buddhism(or at least its sects) but what did he think of the religion ?

Similarly to Ricci,Xavier was not especially enthusiastic about Buddhism.In his letters,he denounced the financial deception of the laity by Buddhist monks and—again—their “sodomy.”While initially tolerant of the Bodhisattvas common in Buddhism,after having Japanese Christians translate the stories of Śākyamuni and Amitābha, whom Xavier thought might have been men “devoted to philosophy,” he decided the two men to be the invention of demons or outright heresy. Xavier was slightly harsher to Buddhism as well in that he did not believe that Buddhism was a corrupted form of Christianity like Ricci but rather believed that Buddhists were almost wholly unable to answer Christian philosophical arguments. In his eyes,they were genuinely incompatible on an almost basal level.In a letter to Ignatius Loyola also written on January 29, 1552, Xavier noted the need for “trained scholars, especially good masters to answer the bonzes’ questions and dialecticians to snare them when they contradict themselves." He felt that Japanese Buddhists were too good in debate and much too stubborn in holding on to their beliefs but was determined to eradicate what he viewed was an intrinsic threat to his work.

Around this point, I'd like to pose another question to this answer: Did Jesuit disdain for Japanese Buddhism see them as "hopeless" or nonconvertible,especially since they couldn't lean on Confucianism "synergy" with Christianity like they did in China ?

Nope! The Jesuits in Japan saw it as a sorta "think of the rewards when we'll finally convert em!" challenge.Records indicated that many Jesuits felt that Japan's religious buildings were nothing short of spectacular and essentially marveled at the potential if such an impressive civilization were to be converted.(I guess that'd give alotta brownie points haha). Luís Fróis,another Portuguese Jesuit, wrote Historia de Japam and Tratado (Treatise comparing morals between Japan and Europe in 1585). He is regarded as one of the first European accounts of Japan in history and his work,although suffering criticism on his bias on certain aspects (I'll explain later) is still useful for a view on how some of the earliest Portuguese missionaries experienced Japan in the tail-end of the Sengoku period.In Historia de Japam ,he has nothing short of awe for the Buddhist temples built in the name of Buddhism.He describes Sanjūsangen-dō as such " The length was of “one hundred and forty braças” and that the building possessed only one entrance, of great proportions. Once inside, the presence of a statue of the Amida Buddha, to whom the temple is dedicated,5 sitting in a meditating position, is immediately singled out. " and goes on to say " They were aligned as if participating in a solemn ceremony, and included interpretations of soldiers and demons". He goes on about Kōfuku-ji,stating that "that boundary is "very strong" made of limestone,with a protruding structure of stone every 8 palms, extending to the outside and to the inside, each supporting a roof of 14 feet (approximately 4,30 m) in width. "None of his descriptions in his works are disparagement but,rather,convey a sense of awe to the reader.It's debatable whether he genuinely liked architecture in general or simply wanted to convey the grandeur of Japan as a potential convert but,in my case at least,the latter's more believable due to his much more gentle treatment of Buddhist structures in particular (as compared to other structures he wrote about)

Now,for the bias problem(as I mentioned above) stems from this: Fróis had arrived in Japan in1563 and had befriended Oda Nobunaga in 1569.He had also,supposedly,witnessed his death in his church (which was opposite Honnō-ji). He claimed that after Oda's death,he became deified as a sorta Shinto/Buddhist deity,a claim which isn't supported anywhere else,not in Japanese sources or otherwise. So why did Fróis have such a claim ? One of the many possible reasons (I've seen many from genuine misunderstanding to pandering to his heirs) that has been guessed at would be that he simply did not understand Japanese Buddhism as well as he claimed he did,in that he generally considered that meritorious men of virtue would be deified upon death in Japanese Buddhism, and simply extrapolated his personal liking or select groups in Kyoto's liking for his patron as general acknowledgement of his "deification". Regardless of this one little loophole in his account that can't be accounted for,I hope this has sufficiently demonstrated that the Portuguese Jesuit understanding of Japanese Buddhism was rudimentary in some,decent in others but generally understood to be incompatible with Christianity.

But wait,what about Shinto ?! This link has what you need https://www.reddit.com/r/AskHistorians/comments/f7fcvm/how_has_shinto_an_animistnature_worshipping/

The TLDR's that Shinto wasn't really a thing in Japan until the Meiji Era with the rise of State Shinto with alotta of the "traditional Japanese rituals" being wholly invented to give the Japanese a unique identity that would see them separate from Chinese and/or Korean influences.During this period (1500s-1600s),Buddhism was the largest religion in Japan by a long mile.

Now for Sources !
1)China in the 16th Century :The Journals of Matthew Ricci 1583-1610 by Jouis J Gallagher
2)The First European Description of Japan, 1585: A Critical English-Language Edition of Striking Contrasts in the Customs of Europe and Japan by Luis Frois, S.J.(Translated by Routledge)
3)Buddhist complexes in the Historia de Japam by Raquel Prazeres
4)From Missionaries to Zen Masters: The Society of Jesus and Buddhism by Trent Pomplun

Edit: Formatting,Spelling,Grammar you know how it is.

Hopefully,someone who specializes in the history of proselytization can help you in the years beyond 1700 but I hope this helps all the same ! Please feel free to ask more if you want more sources!