You might get lucky.
How to remove wall mounted toothbrush holder.
Before you do that make sure that the top and side edges of the holder are t sealed against the wall with caulk or with layers of paint.
How to remove old toothbrush holders from the wall.
You might decide to put up a new toothbrush holder or reuse the one you removed.
When the tumbler comes out cleanly that will be your point of diy pride.
When you are remodeling your bathroom you may want to remove the toothbrush holder from the wall.
Removing bathroom tile shiplap bathroom washroom remove tile master bathroom toothbrush holder wall guest bathroom remodel bathroom remodeling ceramic soap dish.
Loosen the two screws and pull slide the holder up against the wall.
Try a dremel with small diamond cutting wheel.
Best bet is to get the grout out then score many grooves in the old t brush holder with the 4 grinder and diamond tile blade.
In repairs like this i always expect to damage a few pieces.
Remove the mounting plate screws with the appropriate screwdriver.
Then heat the remaining glue and scrape it off.
Try and cut it down to the mortar and or lath.
If they really are glued to the wall a heat gun on low might melt the glue enough to get them off.
Locate the screws securing the toothbrush holder to the wall.
Removing tooth brush holders soap dishes etc.
Score the grout around the perimeter then tap it out with a rubber mallet.
Then say a few prayers and carefully chisel the old one out.