The issue with (C) is that it adds no new information to the argument. The argument already tells us that "we had all the information about them that we needed," which presumably includes information about the materials used in the construction of the mosaic. (A) on the other hand, strengthens the argument because it addresses a possible objection to the conclusion. The conclusion that the mosaics should have been left at the original site is based purely on archeological considerations, perhaps there are other reasons to remove the mosaics, such as risk of theft. (A) counters these objections by saying that the only considerations that matter are archeological and thus strengthens the overall conclusion.
Let me know if this makes sense and if you have any other questions.