We have an old house. In one bathroom, there is a towel rack attached
to the tile wall right over the tub. It's a terrible place for a towel
rack and it has bugged me for years. I am reluctant to remove it
myself, because it's attached to the tile with what looks like the
same cement (grout?) that they use to attach the tiles. The cement is
white and very hard, like grout.

I tried tapping it with a sharpened screwdriver and a hammer. I was
able to chip away some of the cement, but I am worried about cracking
or scratching the tile underneath.

Is there a good way to remove the towel rack?