There are 3 layers in your monitor: backlight, diffuser sheet, LCD.

On top of the LCD layer there is the outermost front facing protective plastic/glass. This is glued on the LCD layer and can't be removed.

Below is freely laid diffuser sheet that you can remove and clean up.

And at the bottom there is the backlight layer that might be removable but I didn't try.

You may find bugs between the diffuser and LCD layer, like I did.