How do you clean rust off of plastic?

I have a tiny fridge that needed defrosted, and stupid me put a metal cookie sheet in it to catch the water. After the fridge was defrosted, I poured the last bit of the water out of the cookie sheet, but then just stuck it back in there until I got a chance to deal with it later. Well, "later" turned out to be 2 weeks or so later. When I lifted the cookie sheet up, there was all this rust there! Apparently I didn't get all the water sopped up when I set the metal tray back in. I don't care about the cookie sheet being rusted - it's old. But my fridge has all that rust in there now. I tried to scrub it off with a wet cloth, but this only took a little bit off.