Okay, one at a time. As for removing the tile, it shouldn't be a problem. It's a matter of cutting the grout joints around the errant tile to remove the surface tension (so that he doesn't ruin adjacent tiles) and then the tile can be chopped out safely.

As for the grout, he would need to scratch the joint out to atleast half the depth, first. The only time you can add new grout on top of old is up to three days after the initial installation. During that time, new grout will definitely still bond with the old. Within the first couple of weeks, it's still hit or miss. After that it just won't work. Right now, you're at that hit or miss stage. But being that he's coming back to fix the tile, why not have him fix the grout properly, as well?

Thanks so much Bill, everyone here seems to need your help.
I wil try to post pictures when done.