Can removal of adhesive tape damage a tile?
If you are talking about glazed ceramic tiles, then the probability of damage is very very low. (There's still the possibility of scratches, if you attack the tile with a blade, but that's not the fault of the tape.)

The only exception I can think of is a small category of rustic tiles that have a very poorly adhered glaze or no glaze at all, but I doubt those would be on the wall.