If the mat boards are just discolored but aren't causing any degradation in the prints, I'd be tempted to trim the mat board close to the edge of the prints and just re-mount the prints with the existing mat board behind it. The dry mount tissue will probably protect the print from any damage from the mat board; I'd hesitate to break that seal.
If you really want to try unmounting them, you can try putting them into a dry mount press at about 200F for five minutes or so, then try separating the photo from the board. Work slowly. If the photo cools too much before you've got it off of the board, you can either put some release paper between the part of the photo you've separated and the board and put the whole thing back into the press, or you can use a (scrupiously clean) clothes iron to keep the temperature up. (Only consider even thinking about having this process cross you mind if you really don't care if the photos will be damaged. If you do care, I'd leave them on the boards they're on and just cut the boards down close to the edge of the photos. It won't be as pretty, but it's likely to be safer.)