American Airlines Model Chrome


Bought a few AA models in the chrome livery off of ebay and noticed inconsistencies in the finish. Some look like they have oil stains but they aren't removable.

Brand new off the factory line the finish is perfect. Do these issues arise because of some kind of reaction between the chrome polishing and the environment? Does anyone have advice on how to 'repolish' these models?
It's what happens when you often touch the polished parts with dirty and greasy hands. Old second hand models have been touched a lot, so a relatively high chance that the polish has stains.
As far as "re-polishing" the models, I'd like to know the answer to that myself. I have a couple that are looking a bit dull, but not stained.