Looks like recidue to me.

I would follow this video guide.
http://www.youtube.com/watch?v=aVEHm325-z8.

What you dont need to do, if you follow the video. Is to unscrew the two screws at the bottom back side of the device, since those are for the keyboard and not the screen. You can leave out removing the "plastic cover" too.

Just undo those 4 upper/middle screws and slide the screen up. Then carefully take the screen out. Remeber how it sits into the slot. This is important to get right when you reassemble.

When you get to the metall rim, take your time and dont force it off. There are clamps that you need to lever out and it will go off quite easily when you get them open.

I would peronally not unplug the ribbons that you find connecing the screens together since you clean it just fine while they are attached. Just softly clean the lcd screen and backside of the touch screen.

If the stains dont go off atleast you know where the problem is and buy a new touch screen.

I have dissasembled my device multiple times and I didnt break it But remember to take your time and dont force anything.