I'm just guessing here but it seems to me if the bath is already dull then it already has minute scratches. Damage done.
It may be possible to fill them with something that doesn't feel horribly greasy when you touch it, but I have to say nothing springs to mind.
I liked Ron's Brasso suggestion. If it can shine brass & chrome to cleam, and remove scratches from CDs, then it may be worth trying. But test in a discreet area first, just in case.
Failing that it's a case of putting up with it. Hardly the end of the world.