Remove damaged grout
Remove grout by running a toothed carbide grit-edge cutting blade, held with firm pressure, between the tiles.

Clean up
Clean the area by vacuuming away dust and washing the area with a solution of warm water and white vinegar.

Apply the new grout
Apply with a squeegee to fill the joints, leaving it to set for 30 minutes, then wipe away excess with a damp cloth.

Leave it to Set
Let the grout set for two days, then apply sealer over the top to finish and protect.