It is necessary to remove existing grout before adding new grout between tiles according to Bob Villa of "This Old House." An existing tiled surface that needs fresh grout between the tiles will require some work.
The reason it is important to remove the existing grout is because grout does not adhere well to existing grout. Placing a fresh layer of grout over an old layer will eventually cause the new grout to flake off away from the surface. The layers of grout will remain separate from each other, which will cause the newest layer of grout to fail.
To prepare the surface for new grout, remove the original grout to at least two-thirds of the tile depth.