This sounds like a difficult job, not impossible but tough, you will have to peel away the card from the back carefully without bending the original.
Once you get close to the back of the print, you can try to roller off the tissue much like emulsion stripping.
A wedding lab is a place to show you how to strip away the print, they do this for canvas mounting, at least before canvas digital prints.
Once again I think this is a job where you want lots of time and patience, It also may be helpful to raise the humidity to assist.
I am not a print restorer and there may be some with credentials that can help more than this Physical Removal Approach.
Originally Posted by tomkatf