There should be four 1/4 hex drive screws holding four black tabs that retain that anti glare screen. Loosen those and lift out the tinted plexiglass.
I clean really dirty monitors with Mean Green (not weak-azz Simple Green), and then follow up with Windex or similar to remove any streaks.
I also clean plexiglass with Mean Green which doesn't leave streaks like Windex can on plastic. If you're really ambitious you can follow up with Novus 2 after removing the cigarette tar deposits with Mean Green.
Since you've got the bezel out, don't take the short cut of cleaning the outside of that tinted plex only, it's probably dirty inside underneath it, as is the front of the monitor tube.