Besides you will feel so much better afterwards and every time you look at it it won't make you thing of how it is just a mistake covered up! Do it the right way! Make yourself proud!
I had a similar situation, the previous owners of my place use natural colored grout and it was stained & had some water marks and looked horrible. I bought grout renew or grout stain and you basically paint it on with a tiny brush like nailpolish. Its time consuming but the finished product looked great. I did this 5 years ago and it still looks new.
Considering that you have just recently applied the grout I would suggest that the best route would be to remove it and go with some color that you like . Trying to match colors usually does not work very well.
Okay, so me and my partner just splurged on new ceramic tile for the Better part of the entire house ( we choose a simple beige tile with subtle grey shades, and a chaparral grout). Well we have the kitchen tiled and it looks great, I grouted most of the kitchen and it looks horrible!!!! Like really really bad. Now I have a decision to make, do I continue to grout the whole house with this ugly color, and then use grout renew to cover it up later......OR take back the unused bags, get grey grout for the rest of the house, and get a bottle of grout renew in the same grey to go over what I just grouted?
Do you think that the polyblend grey grout will match the polyblend grey grout renew...? Since I currently don't own a time machine, I have to make a quick decision before my partner kills me haha!!!