If you're lazy like me, that stuff can get really hard and stubborn after a year or two. It's supposed to be calcium/lime deposits, and is most prominent where water once was and evaporated, leaving the residue.
There are special products you can get from a petstore designed to eat it. A thin, flat razor blade will also do the trick.
it's probably cheating somehow, but i just bring the lids to the sink and scrub them with brillo and rinse them extremely good. plain steel wool would probably be better, no soap residue to worry about. the wool barely does anything to the plastic, much less damage than say, a razor blade.