Clear, clean, water, distilled is best. Take your time, do small areas. Wet the tissue paper, let it soak, then wipe or brush it off, or use a low pressure air nozzle, 40 psi or less, or both. Blot the area with a clean cotton rag, then let it air dry.
This is assuming it is a recent, undamaged, no cracks, etc. painting. If this does not work, go to a conservator.
When you have completed this project, tallied up time spent on it, shop space, etc. Ask yourself if a conservator would have charged what you were planning on charging. What makes you think your time is worth less than a conservators?
Time is time, that's what we sell, our time. It's how we pay our bills and earn our living. Think about it.
I'll bet it is what is called pejoratively "Art By The Pound". It is recently produced (smell the fumes?) classic (read: trite)art mass produced in studios both here and abroad. The distilled water trick should work well on this. On anything else, give them the number of a painting conservator and resist the urge to pick at it.