C.C.
Is/was the grout white? If so, try the Clorox bleach pens. Basically, you draw the bleach/gel stuff onto the grout line, let it sit there for a while, then scrub it off. I did that with my countertops at my old house (white tiles with white grout - in a kitchen - who the hell designs a kitchen that way? Uggggh) - anyway, they came out as good as new with very little effort on my part! Since you're doing a whole floor, maybe there's some way to buy Clorox bleach gel in some form larger than the pens, I don't know...