Originally Posted by heero_yuy

The underlying screen is two sheets of glass with a very small gap of a few thousandths of an inch inbetween where the actual liquid crystal fluid is contained. The delicate bit is the polariser mounted on the front, that is generally made of plastic and doesn't like moisture or solvents and is soft so easily scratched. The manufacturer can advise whether a light solvent like alcohol can be used to remove greasy deposits.

Having said that you don't want to press hard on the screen as this puts a lot of stress on the glass components as well as any integrated electronics.

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