try those err ... paper ... which ladies (maybe some men) use to err .. absorb oil from their faces. i tried that once on my dsc-p1 when i found the lens oily (god knows where it came from). no 'rubbing' required. press lightly on the lens, and bingo! good luck!
i clean it with whatever soft things i could find handy... fingers, tissues, my shirts, or pants, etc.
quite tough to take care of this filter, ven though i have a pouch specially for it. my CPL filter seldom last very long with me, i have lost many pieces liao over the last 1~2yrs....lost 2 during my trip last week. ;<