Cover the adjacent tiles with masking tape to avoid scratching the tile faces during the repair process.
Remove the remaining grout in the joints surrounding the granite tile with a rotary tool containing a carbide grout blade. Turn the tool on, and run the blade in a back and forth motion through the grout in the joint to cut it away until you reach the mortar holding the tile in place.
Slide a small, flat prybar tip into one of the cleared joints. Apply upward pressure to the bullnose tile while slowly moving the prybar further beneath it to push the tile away from the countertop until it lifts free. You’ll need to work as slowly as possible to avoid cracking or breaking the tile. Remove the tile and place it upside down on a flat work surface.
Remove the mortar from the back of the tile with the rotary tool and blade, and then remove the mortar from the countertop area where you freed the tile using the same tool.
Sand the countertop area smooth with a sanding block containing a coarse sandpaper attachment. Wipe the countertop and the rear of the bullnose tile clean of residue with a tack cloth.
Apply premixed thinset mortar to the countertop with a trowel. Press the bullnose tile back into position onto the countertop. Make certain that it is level with the adjacent tiles by placing a carpenter’s level across it. Place a piece of masking tape over the tile to hold it in place as the mortar begins to set. Wait overnight for the mortar to set sufficiently before grouting.
Fill in the joints between the tiles with grout, using a grout float to push the material into place. Wipe the surface of the tiles clean with a damp sponge, wait two hours and then wipe again with the lint-free cloth. Allow the mortar and grout to cure in place for 7 days before touching the tile.