I'm curious as to the starting point of this question where did you hear/read this?

The Inquisition only had the authority to investigate religious crimes (heresy, blasphemy, sacrilege, etc.) As part of that it had powers of censorship over published material in order to prevent texts from promoting or perpetuating such activity. I'm not aware of any systematic campaign against mythologies as such.

Religious authors frequently cited Greek and Roman mythology, recognizing that it had a moral and historical value even though they did not believe those gods existed. At about the same time Spanish religious authorities and missionaries recorded the mythologies/cosmologies of Native Americans and did not receive censure for such activity.

In fact historically, the writings of religious authors have been one of the best sources for mythologies precisely because they cared what people believed especially if that knowledge could be used to spread the faith.

Without a clear citation for the claim made by the question, I am left wondering if the premise is just a myth about the Inquisition and it's activities.