Dig out the grout from around the first damaged tile, using your grout saw to break up the grout's surface and work your way down into it. Work your way around all four sides of the tile, getting out as much of the grout as possible without damaging the adjacent tiles.
Hold the tip of the chisel in the open space along one side of the tile, angled against the line where the tile meets the wall. Tap at the chisel with your hammer. Move the chisel to a different point along the tile and repeat. Continue until the tile comes out. Repeat for each tile you're going to replace.
Scrape the exposed wall with a razor scraper to remove any remaining adhesive or grout.
Wipe down the exposed area with bleach, and then rinse it with water. Let it dry thoroughly before proceeding to Step 5.
Use a tiling trowel to spread tile mastic on the back of a replacement tile, covering the back completely. The mastic should be about 1/8-inch thick.
Set the new tile in place in the open space. Set it so the gaps around it, alongside the adjacent tiles, are consistent on all sides. Repeat for each new tile. Let the mastic set for 12 hours.
Grout the tiles, spreading grout around each of them with a rubber grout float, pressing it into the spaces and scraping it off the surface. Use a damp sponge to wipe up the excess grout.