I use a scratch remover polish GS 27 (as seen on TV) available at Wallmart.
Use Blue Painters tape to protect the black surround.
The thing is, you need to rub vigorously and repeat until satisfactory results are achieved.
Although denatured alcohol works as the others have advised; I don't like using any solvents that might get on other areas that could be damaged.
(Just another tool for the tool box)
Mine had a white type of haze that came off with just a simple rubbing with a stiff old towel. I was surprised that it came off that easily. A little still on the edges, but 99% clear. Might have been the exception.
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