I just wonder if the grease/salt has actually eaten the finish off the drip pans. They may look rusty because that is actually what it is. I would guess that they are probably stainless or polished aluminum. They may also be plated. Thin coating over cheaper metal.

On that note they do make chrome polish for autos. Depending on the cost, you might just look into replacing them.

Those catch pans are just chrome plated and I'd suspect over the years the chrome has worn off and the base metal under the chrome is actually what is rusting.

You may just want to replace them.

I'll buy new ones. I've seen them in a local hardware store. Thanks for the advice.