Tough to advise on cleaning. I think you could try a cotton swab or similar with detergent and cool water (as you'd use to clean) and just dab this on a bit of the painting. See if it budges at all—if so, you can't clean it. If it doesn't come off on the swab, it still could crack or flake off if bent, so cleaning is iffy. Ink stains can be removed with specific ink removers depending upon the type of ink. Water-based inks can come out with laundry detergent, ballpoint and felt tip marks sometimes respond to isopropyl alcohol alone, which you can apply to the mark with a cotton swab. I also use Carbona's Stain Devils #3, made for ink marks (not sure if that's available to you).
The problem with all of these is that any liquid will leave a ring mark on your satin. There is a way to soften those ring marks—if you think you'd like to try spot cleaning, I'd be happy to tell you more.