How do I remove dark gray traces in the upper screen corners?

The previous owner of this iMac was a heavy smoker. Thus, in the upper corners of the display you can see dark grey traces of, I guess, nicotine.

I have dismanteled the iMac according to the Apple Service Manual in order to be able to clean the surface inside the protective layer. However, it looks as if the TFT-screen and the protective layer are welded together. I have not been able to take them apart to clean the surfaces.

Is it possible to take the two screens apart so that they can be cleaned? If yes, how?

Kind regards,

Kurt