I recommend contacting
The CRT Collective Facebook group for this type of advice.
Be VERY careful, some CRTs have an antiglare coating. Once you buff that out, you will have a very odd "shinier spot" where the scratch used to be -- and that's much worse than the original scratch. Not all CRT tubes have this, and thus there are solutions for filling/buffing out minor scratches.
With certain types of CRT glass, sometimes you can do a temp "hide" fix by rubbing super clean Vaseline (buy fresh petroleum jelly, and put then a bit into a brand new lintfree cloth that has never been used to wipe dirt, then rub the scratch). That "wets" the scratch in a way that doesn't dry out, and turns the scratch "invisible". Sort of like those windshield crack/scratch hiding solutions. Others have resorted to toothpaste as a glass polish (or other ultrafine abrasives, in increasingly finer grit steps). But on some types of antiglare-treated CRT glass it makes things worse, while on others it makes things better. Polishing antiglare films require completely different substances than polishing direct glass. You MUST choose the right solution for the right CRT and right antiglare coating, or you are going to make it look worse.
Close seconds are "Vintage Television Collectors"
Post a photo of the CRT (whole CRT, plus close up of scratch), and the model.
Some expert may chime in with model/type-specific instructions for your scratch, if there's a possibility.