who is your blanket in the cold of the night?
Ask your local fire department.
The problem is that the grout was never sealed. It is very porous, and the stains may have gone deep into the grout. I'd be curious about CLR. I've used it for other stuff, but it will likely affect the color as well. If it's really bad, the best thing is to scratch the grout (with a hand grout tool for a beginner), and take the level down a bit. You will be exposing cleaner grout. Then mix a batch of matching (as close as possible) grout and go over all the grout lines with it. By having clean grout under, the new grout should adhere properly. Go at least 1/8 of an inch deep. It's a bit labor intensive, but short of taking it all out, you'll not get a closer match. Be sure to seal it 2-3 times when the grout has cured. When a drop of water isn't really absorbed, it's sealed. Then re-seal 1-2 times per year to maintain it. Use Sealer's Choice 15 Gold to seal it, available at HD. The other option would be to stain the existing grout to match the stains. The tools and instructions are readily available at the usual home improvement stores. The whole thing would take a weekend, assuming it's not huuuge. Good luck with that.
