This is a good question! Church history is a favorite topic of mine: I have a degree in Art History, and am currently working on my Masters of Divinity. The question of whether the Catholic Church had the power to do so is rather hypothetical. If they were ever successful in completely erasing some document from history, it would be impossible to prove. What we can do is look at instances of censorship we know about, and draw conclusions from there.

Late Imperial/Early Medieval Period

Although he predates the period you have asked about, most church historians will immediately think of Origen as one of the key examples of censorship by the early Christian Church. Origen himself was a theologian and teacher who lived in Alexandria and died in 254, but the controversy that resulted in the mass censorship of his writings came to a head in 6th century. In the years since Origen's death, Christianity within the Roman Empire had significantly refined its doctrines. In 543, a regional council in Constantinople condemned a group of self-proclaimed "Origenists", a ruling which was confirmed by the Fifth Ecumenical Council in 553.

The latter also posthumously condemned Origen and his writings, which resulted in the large scale destruction of his work. This was easier said than done, and only partially successful. Several commentaries and works of Origen that had earned the endorsement of other great theologians largely survived: the two most famous examples being Origen's De Principiis as well as the Philocalia which had been compiled by Basil the Great and Gregory of Nazianzus. However, we are aware of several texts that were more or less completely wiped out. The most famous example is the Hexapla, which was a compilation of the Old Testament which compared six different Greek editions in parallel. Only fragments survive today. We know of the existence of the work primarily through other writers, notably St. Jerome, who compiled the Latin Vulgate translation which would serve as the primary text of the Roman Church until the Council of Trent in the mid 1500s. We also know many other texts are missing, but it can frequently be difficult to specific exactly what. For example, Origen was condemned for teaching that souls existed in eternity before the body, and also that salvation would be universal in it's effect: even Satan himself would be redeemed. It's hard to say if this is true or not. If Origen taught these ideas in any seriousness, there is little to no record of it. If he did, the texts were likely all destroyed, but it is at least equally likely that such teachings were taken out of context by later followers, or fabricated completely.

High Middle Ages and Reformation

Although the Pope had been the dominant religious Authority in Europe for several centuries, papal supremacy reached a new level of authority after the break with the Eastern Church in the Great Schism of 1054. Yet in the context of your question, it also limited the Pope's power as far as censorship was concerned: the Pope had no ability to enforce any attempts at censorship in the Christian East. Even after the Islamic conquests, most Eastern monasteries were allowed to continue their activities with little interference from their Islamic rulers. St. Catherine's Monastery in Sinai, and the collection of monastic communities at Mt. Athos in Greece held and continue to hold great archives of manuscripts, relics, and religious art. So even if the Roman Catholic Church desired to completely destroy certain records, if those same documents existed in the East they would be preserved.

That doesn't mean the Roman Church didn't try. The existence of documents in the Palestinian desert was of little consequence to the average citizen of Western Europe, and so in practice the Roman Church still practiced censorship frequently and extensively. Condemnation of heretical teachers or groups was often met with the widespread destruction of works associated with them. Of course, by publicly ordering the destruction of such works the Catholic Church simultaneously guaranteed records of their existence. It is also important to note that even the Catholic Church was often not powerful enough to fully stamp out dissenting factions. Groups like the Waldensians and the Hussites were frequently able to survive in isolated communities in the country side, or under the protection of sympathetic rulers.

In regards to supporting Papal authority, the most difficult problem facing the Catholic Church was the discovery that certain documents which were used to bolster the Pope's claims were outed as forgeries. Starting in the 800s, the Roman Church had been using a collection of documents, known today as the Pseudo-Isidorian Decretals, were demonstrated to be forgeries by Cardinal Nicholas of Cusa. Of course, with the advent of the printing press and the breakout of the Protestant Reformation, Rome lost even more control over the circulation of unwanted documents: whole nations defected to the Protestant cause, and even within largely Catholic countries, the printing press made it impossible to completely stamp out unwanted publications. The same held true for Catholic documents in Protestant countries.

Post-Reformation

Yet, the Roman Catholic Church had one further tool it used to censor documents: the obedience, faith, and loyalty (although some would say fear) of its adherents. In 1557, Pope IV issued a list of documents and book which Roman Catholics were prohibited from reading, or even possessing without special permission. The Index Librorum Prohibitorum was continuously updated and revised over the centuries until 1966, when it was discontinued. The final edition is incredibly extensive, including not only the Protestant Reformers, but also later philosophers and scientists whose works were considered "contrary" to Catholic teaching.

Summary

In summary, it is highly unlikely that the Roman Catholic Church ever managed to completely "wipe it off the records" as you put it. Most attempts at censorship created records of the very things being targeted. Even in cases where the Church was almost completely successful, the existence of Christian groups outside of Rome's control almost always assured their existence in the long run.