PME wrote:

No, there are no screws. This is a solid chrome plated insert. There are
rivets holding the cup-holder onto the fixture, but it's loose enough to see
the rivets have nothing to do with the wall attachment. There is definately
something inside the wall holding this.

Are you planning to reinstall it, replace it or fill in the hole?

Fill in the hole:
Cut the drywall around the soap-dish and remove the whole shebang. The
drywall patch will be a little larger, but so what?

Replace it:
Cut the existing dish up with tin snips and remove it in pieces. Could
be a pain in the ass depending on the thickness of the metal. You
might get lucky. If you use a larger dish than the existing one, you
could combine the first these first two methods.

Reinstall it:
Do you even have to remove it? You might be able to glue it back in
place and cut the wallpaper around the dish. Use stronger adhesive
around the cut edges to keep them from curling up in the moist air of
the bathroom.

R