Are you the original owner? Could it be that a former owner applied some sort of protective film that is now failing?
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It does seem like some sort of thin protective film. If I manage to peel it off (without a razor), then what? I'll have to deal with the faded lamps left behind. Where do you buy this film - and will that hide the faded lamp? (Or can I just clean the lens with a toothbrush and toothpaste or lens restorer?)
You will have to deal with some slight left over adhesion from the film. Thinner works very well when it comes to removing adhesive residue, just use a rag to remove the left over adhesive after you remove the film before you start the restoration process; otherwise the residue will gum up the sand paper. If your lens is yellowed due to the sunís UV rays, you need to restore them back to their original condition by using a lens restoration kit. I personally have used the 3M product on my wifeís Prius. Here are the results. You can get the clear lens protection from a tint shop. Use Yelp or the Yellow Pages to find a shop in your area.
I would take a hairdryer and try to peel up a little corner of the film and see if a little heat will help soften the adhesive. That should help you get it off. Shops use a little heat to remove graphics and paint protection films.
As for restoring lenses, I have also used the 3M lens kit with great results.....great product.