Cut a paint stir stick into thirds with a utility knife. The shorter lengths are sturdier and easier to use.
Wet the affected area with water from a spray bottle. Cover nearby desirable grout with plastic to avoid getting the new, uncured grout wet.
Place the edge of a cut paint stick on the outer perimeter of the affected area. Push the edge firmly and aggressively into the grout clumps with short strokes. Keep pushing until the majority of the large clumps lift from the surface. Keep the area moist as you work. The grout will eat through the paint sticks. Change them as necessary to keep a sharp, cut square edge.
Wipe up the removed grout with a wet sponge. Scoop the grout up. Do not drag or scrub the grout. You may scratch the surface of the tile.
Wet the area again. Scrub the remaining grout up with a scrubbing sponge. Keep the surface wet as you scrub.
Wipe the area clean with a wet sponge.
Buff the area dry with a clean towel. If the towel snags on residual clinging grout, repeat the previous two steps.