Use a carbide grout saw to dig the grout out from the perimeter of each tile that's loose. Press the straight edge of the blade against the surface of the grout and push and pull it forward and back, while applying downward pressure, to break up the surface. Get as much of the grout out as you can.
Press the tip of the chisel against the base of the tile, at the loosest point where the tile is moving. Tap the chisel with your hammer to work it under the tile. Move the chisel to other positions around the tile as it continues to loosen, until it pops out completely. Repeat for each loose tile.
Remove any residual mortar from the area where the tile was taken out, chiseling off the mortar with your hammer and chisel. Clean up the back of each of the extracted tiles in the same manner.
Apply a layer of tile mortar on the back of one of the extracted tiles. Make the mortar about 1/8 inch thick. Press the tile into place on the surface where it was before, spacing it evenly on all sides with the surrounding tiles. Repeat for each of the extracted tiles.
Let the mortar set overnight. Re-grout the spaces between the tiles where the grout was extracted, using a grout trowel to force the grout into the lines, then wipe off the excess grout with a damp sponge.