I say its time for a new monitor................

J/K I believe what they fill windshields with works because its really two layers of sandwiched glass and it manages make something glaringly bad much less annoying. But the background of the monitor is backlit by the video output so I don't think you will ever get it to be completely not noticable short of doing glasswork and then polishing and recoating the entire screen.
But any kind of clear drying epoxy might make it less noticeable (but if it bends the light different than glass it might be even more annoying). You could also try clear nailpolish, but beware the coating can be harmed by any harsh chemical. I might just find me some polish (like what they sell to reduce the scratches on cd's and rub a little in and hope it lessens it enough to not bother you anymore. It would really suck if you made it worse by trying to fix it though.