I have always removed the rings from my jars, whether pressure canned or water bathed. If you want to pretty them up for gifts, you can cut a circle out of fabric using pinking shears, lay it across the lid, and rescrew on the rings - loosely. A good way to store your rings (after washing and drying as chickhill noted), bend a metal clothes hangar into a loose circle, unwind the top twist and thread them on. You can re-attach the twisted end loosely and hang in a closet or other out-of-the-way spot until needed again.
