2001FP: Protective plastic layer causes problems?

There is obviously a plastic protective layer on top of the LCD, and it seems to cause some problems.

For one thing, it seems to be not trully clear/transparent, similar to old glare/radiation filters, consisting of very small cells.

Secondly, you can notice that it is not evenly colored by slowly dragging around a large window with white background (e.g. Notepad).  Look closely, and you will see that the white Notepad background changes its color as it passes under different areas of the protective layer.  If there were no protective layer, or if it were made of clear glass, the white color would look the same regardless of where the window is positioned on the screen.  I had the same issue with a Sony Trinitron monitor (2 years old) which has a thick protective/antiradiation coating, and it's not 100% even in different areas.

I wonder if I can open the monitor and take off this protective layer.

Ideas?  Anyone else notice this problem?