There are a number of grout cleaning agents that are acid-containing (oxalic, muriatic). These will destroy marble, so avoid them. Heavy duty emulsifying cleaners are highly alkaline and may not damage the tile. You should test in an inconspicuous area. For new looking grout, you can purchase a grout saw (small hand tool) that can be used to scrape out enough grout that new grout can be applied. This will give you a brand new surface, but must also be sealed to make future cleaning easier.