Flooring Tile - HELP!!new baseboards and old grout

I am redoing the baseboards in the guest bathroom in an old house. The flooring is tile, and they have grout running all the way up to the baseboards with about 1/4" gap to drop the baseboard in. In other areas, the tile runs all the way up to the baseboards. In both cases, the grout forms a lip when it comes in contact with the baseboards and is not level with the floor. My question is: should I knock down the old grout that touches the baseboard and regrout it, or leave the old grout and just run a bead of caulk on it. I am leaning towards knocking the old grout out and just putting in caulk in its place, but dont know if thats a no-no or not in a bathroom. Over the years, there has been a little water that has dropped down and rotten out some of the baseboard, so im concerned that putting the grout back in will allow it to continue to get water. Dont know know though. Thanks for the help

You are better off to fill the gap with caulk. The seasonal movement of the wood in the walls will push on the grout causing a tile to possibly come loose or crack under the sideways pressure