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The tile should be ok if you protect it but can understand why you'd be reluctant. The other option is a set of grips on the accessory and give it a good tug. In all likelihood the tile has been drilled with a diamond bit then the wall behind it drilled and plugged so you should be able to pull it off the wall.
Have you tried getting something to lever it off? You could even try a pry bar or similar as long as you have a piece of card or thin ply between it and the tiles.