Leonard,
I've had good luck over the years cleaning a variety of things with a PASTE of Comet cleanser. Wet a 3M nylon scrub pad and then shake a tablespoon of Comet powder on it and work it in with your finger. Then rub this directly on the spot, using liberal amounts of pressure on the sponge in a circular motion.
It may take a few trys, but it should remove the spots.
Spot