This is a fascinating and complex issue because of course there is no uniform Christian view of Hinduism at any point in history, let alone over 400 years! So what I am going to write here is not meant to be a comprehensive answer, but rather to provide you with a selection of interesting and relevant examples to give you a sense of the range of attitudes.

Up until the 18th century, Europeans called all religions that were not Christianity, Judaism, or Islam "Gentoo" religion, "Heathen" religion, or "idolatry." When the Europeans encountered new people, they would frequently be unsure of whether or not the practices of particular social groups should even be called religion. European travelers during this era would sometimes provide very brief and questionably accurate accounts of the religious lives of people in India, usually derived from casual observations and conversations rather than serious study. When these travelers were missionaries, their accounts were unsurprisingly very negative and focused on the importance of bringing Christianity to the region. I actually just learned at a conference this weekend that Protestants in particular tended to view Hindu traditions as being analogues to Catholicism, surprisingly enough.

On the process by which Hinduism and other religions came to be a legible category for religions, Tomoko Masuzawa's Invention of World Religions is incomparable. JZ Smith's "Religion, Religions, Religious" is an outstanding essay on the development of the category religion.

By the time you get into the 19th century, things changed quite a bit. You have a rapidly expanding body of knowledge about Hindu traditions in European languages, especially English, French, and German. This followed the foundation of the Asiatic Society in 1784 by William Jones. This organization gathered a substantial archive of important literature and published a journal called "Asiatick Researches." To a substantial extent, European scholars considered religion to be whatever was written in ancient texts and so they focused very exclusively on studying Sanskrit literature. They would often rely on the assistance of pandits to pursue these studies. Meanwhile, in 1813, the British began to permit Christian missionary activity in India. It had previously been forbidden as a threat to the stability of lucrative commercial ventures in the region.

Generally speaking, European representations of India fell into two broad camps. One camp thought that India had never produced anything of merit culturally speaking and that Indian culture and religion needed to be replaced as much as possible by European culture and Christianity. Thomas Macaulay typified this attitude. In 1835, he famously argued in his "Minute on Indian Education" in British Parliament that the Indian education system should be gutted and replaced with a British system:

"The question now before us is simply whether, when it is in our power to teach this language, we shall teach languages in which, by universal confession, there are no books on any subject which deserve to be compared to our own, whether, when we can teach European science, we shall teach systems which, by universal confession, wherever they differ from those of Europe differ for the worse, and whether, when we can patronize sound philosophy and true history, we shall countenance, at the public expense, medical doctrines which would disgrace an English farrier, astronomy which would move laughter in girls at an English boarding school, history abounding with kings thirty feet high and reigns thirty thousand years long, and geography made of seas of treacle and seas of butter."

Monier-Williams is another example. He wrote in the preface to his Sanskrit-to-English dictionary that the only reason to bother with such a massive undertaking was to more effectively convert Hindus to Christianity, and certainly not because there was an merit in the entire Sanskrit literary corpus.

Another type tends to romanticize ancient India and so seems more positive, at least on the surface. The German scholar Max Muller is a good example of this type. Muller absolutely admired classical Indian thought, even if he believed that Indian culture and society had fallen into a steep decline since. Like other romantics, he viewed Indian literature as containing magic and mysticism that could answer the disenchantment of European modernity. Critics would point out that people like Muller only cared about Indian literature and thought inasmuch as it could be appropriated by Europeans to solve European problems.

So much has been written about all of this. In general, Inden's Imagining India and King's Orientalism and Religion would be good places to start. Some of it is also covered by Masuzawa, which I mentioned above.

OK, I feel like I could go on for a while about that one, but I want to provide one more short vignette specifically on the idea of Hinduism providing theological challenges for Christians. One of the first big name public Hindu intellectual who took on Christian missionaries was a man named Ram Mohan Roy (1772-1833). Ram Mohan Roy had internalized the idea that monotheism was superior to polytheism, and propagated a monotheistic interpretation of Advaita Vedanta as the correct version of Hinduism. Having formulated this monotheistic Hindu theology, he was fond of castigating Christian missionaries for their trinitarian beliefs. Belief in a trinity, according to Roy, was less monotheistic than Advaita Vedanta. At that time, a lot of liberal Christian intellectuals were already embracing a unitarian theology. And there was one Baptist missionary named William Adam who was so persuaded by Roy that trinitarianism was polytheistic that he converted to unitarianism! So I would definitely consider that an example of a Hindu posing a theological challenge to a Christian, but maybe not in the way you mean!

A short postscript to that story: at that time (about 1821), the Boston intelligentsia leaned heavily toward unitarian Christianity, including one Ralph Waldo Emerson. The story of Roy converting Adam caused a massive stir in the American Unitarian community, who at that time had less access to information about India than their European counterparts. They didn't know much about Hindus, but they either they had some natural inclination to Unitarianism or otherwise they were their allies against trinitarianism. Roy's conversion of Adam thus became the beginning of the American process of romanticizing India, which Emerson and later Thoreau gave voice to in the Transcendentalist movement.

On the process by which Americans came to gain a sense of what Hinduism is, Michael Altman's Heathen, Hindoo, Hindu: American Representations of India: 1721-1893.