If the print cannot be reproduced I would not try to remove it. I have a couple of signed Ansel Adams prints that were purchased already mounted and later over matted at a frame shop. In both cases it appears to me that acid-free board was not used (even by AA). The board is not pristine but there is no damage to the prints. I have had them for 40+ years.
IMO, if it's not broke don't fix it. If you are going to display them use an archival over mat.