The grout will actually come off easier if you let it dry. You can then brush it off with a soft wire brush in circular motions, then again with a nylon brush. Wipe your mosaic of with a clean dry cloth in the end.
Lovely, lovely piece!! Just want to say the music is a bit loud and some of what you say is indiscernible. I love the technique and will try a piece like this! Thanks for the tips.