It's hard to tell in the picture, since its a little out of focus, but if it's just a scratch in the outer layer not affecting the pixels underneath, you might be able to fill the scratch using a plastic scratch repair kit. Results might vary depending on how deep the scratch is and what sort of finish the panel has.
Another option if its just a surface scratch would be to apply a bit of vaseline / petroleum jelly to the scratch and wipe off the excess, which can similarly hide the scratch, though in a less permanent way.
If the pixels underneath were affected though, which that rainbow color might potentially indicate, there might not be much you could do to fix them, short of replacing the panel, which is generally the most costly part of a monitor, and potentially a bit difficult to do. Depending on the cost of the panel, it might be better to simply use the opportunity to upgrade to a new monitor, and relegate that one to a less-used system or something, if that's the case.