I have never tried any sort of steel wool, but I put very very fine scratches in my Rinehart pipes with my fingernail trying to get toasted bug guts off them. I'd bet some very very fine polish could fix the marks tho.
Anyway, I've tried various white cream type chrome polishes from turtle wax to mothers and maguires. I finally tried Nevrdull the other day and damn that is by far more effective and easier to use than the other things I've tried.
HD bright chrome cleaner works well for me and then a coat of wax. Also I have had good results with a product called white diamond! And again after using that product put a coat of wax on to protect it. Imo
If you really need to "CLEAN" your chrome, a magic eraser works well and will not harm the chrome. Then just pic a chrome polish you like, have experience with and run with it. Definitely DO NOT use any grade of steel wool on your chrome.