Banana Peppers - Canning

We canned banana pepper rings and sealed them using the hot water bath method and for some reason stored the jars in the refrigerator. If we remove them from the refrigerator, will the peppers still last as long? The “mixture” we used in canning is just white vinegar, salt, and water, and the jars are still sealed.

If they were properly water-bath canned with a vinegar brine, they should keep a long time in a cupboard with no refrigeration. (How long? IDK, but a year anyway.) Quality will suffer if they are stored someplace warm or in the sun.

I dont see a problem.  You have stored them in a cool, dry place.  Moving them to another location should not be a concern

Oh yes, welcome to the site.