How do you remove a towel bar that has no visible screws?

How do you remove a towel ring from a set screw?

How do you remove an old towel rack?

How do you get a glued towel bar off the wall?

Use an oscillating multi-tool to cut through the adhesive between the wall and the towel bar holders. If absolutely necessary use a hammer along with a chisel or pry bar to pop the towel bar holders from the wall. Sand adhesive residue off your wall with 100-grit sandpaper.