All you can do is Contact cleaner ... or Ethanol .... liberally apply to plug ... and insert / pull out repeated .. applying cleaner repeatedly .. wipe away crap as it comes out.
You can get glassfibre pencils from electronics suppliers, or use a rolled bit of very fine wet'n'dry paper to clean up those outer connector rings... but... that will reduce any remaining corrosion resistance that might be left from plating on the connector surface.