There is a special grout which resists stains. It feels and looks a little different from regular grout. It costs much more too but well worth the money spent. Installers don't like to "work with it" but insist on it. They won't be living with it but you will.
I know this is an old post but in case anyone else is searching for this like I just was ...
Yes, you can cover them with tile. I would go to a Home Depot and ask them. Probably just sand it down a little. Apply the glue, tile, then grout. Be sure to seal really well to keep from staining. Use a darker grout also. You'll love it!
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