Well, I don't know for a fact that it'll work on your Polar, but there's something for iPods called iPod Polish or Apple Sauce or something. It's scratch "remover" for iPods. (It actually fills the scratches in so that they don't refract the light.) If I were in your shoes, I'd try that first. And then I'd get a tiny piece of 3M Paint Protective Film and apply it to my Polar. (This is the same stuff that Invisible Shield is made from.) In fact, I think I'm gonna do that part right now.
Sorry to be a pest, but it's "affecting," not "effecting."
