<p>If it is brand new, what is the warentiee? You might be able to return it. I'd check that out first.
<p>Can you live with it as is? If not I'd try a glass wax first, which might fill in the scratches good enough that you can live with it. With some smoked plexi over the monitor and perhaps it will be invisiable.
<p>Last resort is to polish the glass, but I don't like the idea of that. Polish works be removing glass. CRTs are can implode if the glass is weakened too much. Obviously there is a margin of safety because the scratch didn't cause it to implide, but how much is there I don't know. A really deep scratch might need so much polishing that you weaken the tube too much. I don't know much about it, but I wouldn't do it unless I had verified I wouldn't go past the margin of safety with my work.