It depends heavily on how the print was made.

For many inkjet prints, there is usually no safe way to remove adhesive once it’s on the image surface. Inkjet inks can be vulnerable to solvents and moisture, and the adhesive may bond to the ink and paper, so cleaning often damages the print.

Some print types are more durable, such as certain laser or dye-sub prints, but even then there’s no guarantee a cleaner will remove adhesive without harming the surface.

For general grime like fingerprints or oils, a print cleaner such as PEC-12 is commonly used for photographic emulsions and may help. It is intended for photo materials, but its effectiveness on adhesive is uncertain, so test very carefully on a corner or noncritical area first.

Going forward, mounted display prints are often protected with a spray sealant or laminate after mounting, which can make later cleaning safer and easier.

So: for adhesive on an inkjet print, the outlook is poor; for normal dirt on suitable photo prints, a dedicated archival print cleaner may work.