Yesterday I was assembling a set of clear mount stamps,the peel-off piece from the back of the stamp (which I usually discard) looked large enough for me to fix one that had torn on another stamp which has a sticky back.
So I placed the new piece over it.
traced around the outline
then cut out the new piece.
Last step was to place the new piece on the stamp.
Now I save all my larger pieces of backing for who knows what other handy solutions.