A steel wool pad will only roughen the surface and let the coffee and tea (even worse) stains attach themselves.
Honestly, Shil, I have never experienced tea or coffee stains, and this part of London has quite hard water, since I bought a dishwasher,
I am not being facetious, and neither would I lie to you, my dear friend (Would I?).
There's something in those 'Finish' dishwasher tablets that would make the angels whiter and cleaner (and probably sing better).