I had a quilt for our bed that wasn't large enough so I made a strip for each side, backing, batting and pieced top to match the quilt. I made each strip the length of the quilt and about 14 inches wide. I didn't remove the binding but stitched the new panels on, stitching in the ditch of the binding. It really gives the quilt a nice look.
I do think that people don't realize the work that goes into a quilt, however, and assume it would be simple to fix. Sitting down and discussing possibilities before you do anything might be a good way to begin.