You could try a tiny bit of acetone nail polish remover on a q tip. BEFORE you try it on the paint, try it on an inner hem to be sure it doesn't alter the fabric itself. If it remains unchanged, do a tiny amount at a time, only adding more remover as needed to do the job. Change q tips frequently. After you are done clean the areas with mild soap on a damp sponge to remove any residue. Not much to lose at this point, unless you would wear it with the paint on it if you cannot get it out.
Could you just mark over the silver lines with a black "Sharpie" permanent marker? I'd try just a dot on the end of a silver mark to see if it would possibly cover it up. If it seems like it would work I'd carefully just cover the silver lines and not get ink on the adjacent material.It might need two "coats". Good Luck!
Take the jacket to the cleaners and have them look at it. They might not be able to do anything for you, but it can't hurt. If this is the case, perhaps you can be creative with ribbon or trim?
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