Removing the old grout would be almost impossible. There is a tool available in B&Q etc for removing grout, don't waste your money, it doesn't work. Your best bet is a wire bristled brush. Looks like a toothbrush (also available in hardware stores) Scrub thoroughly with soap, water and bleach. This may do the job. Re-grouting probably won't work as the grout has to go all the way between the tiles to adhere properly. If it is just on top of the old grout it will more than likely crack.