I just recieved a FW900 24" CRT monitor from ebay (HP branded for you nerds out there -) ) It works perfectly, but there is a small scratch in the middle of the screen. It is only noticable if the screen is all black or all white, but it is kinda annoying. There is no anti glare coating, so I don't have to worry about that getting in the way. How would I go about removing this scratch?
You can't "remove" a scratch from glass, at least not without polishing (abrading) down the surrounding glass to bring it to the same level as the scratch. Your best bet is to use an optical-grade polish or epoxy that is often used for things like eyeglass or windshield repair. It fills the crack and then you buff it out. It probably won't remove it 100% but it might reduce its appearance.
Note that most CRT's have a coating of some type, it might just be clear and you can't see it. If the coating is scratched, especially if it's not 100% clear, you likely won't be able to hide the scratch.