Plenty of grout colorant stains on the market.

My husband and I used a paint-on (tiny brushes!) grout re-colorant from Lowe's on a stone floor where overuse of wax stained the original grey grout to yellow. We stripped the wax as best we could, then painted on the new grout color. Not hard, just tedious. There are also franchise companies, like Sir Grout and The Grout Doctor, that do this kind of work if you want to get quotes.

@Creative Tile Eastern CT, should I just color the grout or also fill it up a little? Can I fill it up? its very deep I think. what kind of color would you suggest for this, beige? or white?

I would do a platinum color (light gray)

I think the robo vac is not going to work for you. Maybe a different model or brand could work without losing brushes?

When you change the tile, you smash and ruin things below it, too. I know I would not trust an electric heat mat to work after pulling out and replacing tile. Check with companies that do hydronic floor heat to see if it is possible to remove and replace the tile without damaging the hydronics. You may find that you are stuck with your tile, or face a huge expense in replacing it.

Creative Tile is the expert. I would take his advice.