No experience, I'd take a diamond blade grinder and cut grooves then bang with a hammer. It will snap in the grooves. Not sure what you'll find behind but chance it will be a long porcelain come or bolt. There will be a spot left.
I don't understand how your comment is supposed to be helpful ?The time to remove the unwanted tooth brush holder was when you were going to re-tile and not a day sooner.
Now look what you have.
Thanks Astora. I've been waiting for your advice since January 2020 !!!! Just kidding. Thanks.Tiny nails and screw holes are the easiest to fix. You can use a putty knife to fill them with spackling or wall joint compound.