In reply to Tony the Blade:
Tbf if anything its probably added to the waterproofing. Any idea what kind of paint it was, e.g. oil based or water based?
I fear with paint that if its had time to dry it may well come to be a permanent feature of your jacket.
The only thing I can think of is gentle rubbing and scraping with a mild solvent (ethanol perhaps) and move on up to acetone and white spirit. Your DWR will get absolutely ruined but the membrane should be resistant to this*, not sure how the bonding of the face fabric will handle it tho.
*depending on if its ePTFE or this newer Gore Tex ePE membrane.