OP, if you want to do this yourself, I highly recommend Grout Shield
Grout Shield | Grout Restoration System | Grout Cleaner, they can match the color of your existing grout. I cleaned and did all of the grout in our house, and the color match was so good that I had 3 areas where I missed putting the "paint" on the grout, and only found it when I was doing the clean up, the uncoated areas turned dark when wet. The kit is below $100.
If you call home warranty, you can get the name of the original grout color, as an alternative, I think there are color charts at Home Depot and Lowes, then just give grout shield the name and they custom mix to match.
Send me a PM if you want more info.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV.