Hi Lynne,
Have you seen the two arrow signs in the ring selection box, this changes the finger and if you keep pressing it it changes the hand as well. Also on the Bracelet icon there are two arrows to change hand.
Just select which finger the ring is on, and press the X in the corner of the icon to remove it.
If you do know about this, then there is a little glitch that a few people have experienced that they can't take off an item of clothing. But to my knowledge it has only happened with clothing.
If the ring / bracelet is still there after doing this then message to support..
OH! there is something else as well. But I'm guessing you've done it. After trying to remove the ring / bracelet have you pressed save ? yeah I know stupid question, Sorry.