One possibility is that the ring against the wall snaps on and off, and that there is a set screw under there that is holding the bar to a hidden bracket. If you try to pry it off, work your way around it and don't use too much force. Also, make sure to put something against the wall to cushion any prying tool, such as a wooden shim. If you pry directly against the wall tile with a screwdriver or small pry bar, you could crack the tile if the tool is in direct contact with the tile.

Alternatively, the ring might unscrew. To try this, put some electrical tape around the jaws of a pair of channel lock pliers, and also give the ring a couple of wraps of tape to protect the finish from being marred.

"Alternatively, the ring might unscrew. To try this, put some electrical tape around the jaws of a pair of channel lock pliers, and also give the ring a couple of wraps of tape to protect the finish from being marred."

I'm betting on this!