I would pull off the old covering. The foam should be OK, but you may want to put a new layer of batting over it. If the foam is yucky, go to Michaels or MJ Designs or Ben Franklin Crafts or JoAnnes Fabrics (or where ever else) and get new foam. It usually comes in the size you need, if not, buy a bigger piece and cut out the size for your stools. Make a template or pattern using the old foam. Then use an electric knife (not just for turkeys anymore) and cut out your new piece. Covering the foam with batting makes it look better under the fabric and easier to position the material. Then staple away! I did my dining room chairs last year, it was very easy.