Want to Remove Towel Rack (but not the underlying tile)

I have a towel rack in the shower stall of my bathtub. It's strategically located such that every time I raise and lower my arm, my elbow comes crashing into it. Long story short, it needs to go.
The towel rack has two mounts cemented (or otherwise glued) directly to the ceramic tile. As the tile is in good shape, I don't want to damage it. How can I remove the two mounts without damaging the underlying tile?
Thanks in advance.
-jk
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the
Are these mounts ceramic also?
If yes, they may be mudset and non-removable without leaving a hole in the tile and wall.
--
Colbyt
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contrapositive wrote:

if they are mudset then you first get some tile to match.. and then break up the mount for the towel rack and then grind out the back of it to make space to put some mud in and let it harden, leave enought space for the new tiles you gonna put in there to cover where the mounts were.
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