Tearing out the entire tiled area only for some damaged tiles is not really, a good idea. It is not too hard to replace the damaged tiles and you can do it that if you have some basic skills and patience.
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You need only, to chisel and break off the damaged tiles and install the new ones. It would be perfect if you have kept some original spare tiles.
If not, make sure your new purchased tiles and grout match with the existing grout and tiles.
Materials & Tools
Tiles; grout; grout float; masking tape; big nail; chisel; trowel; hammer; sponge
Steps to Take
1. First step is to tape the perimeter of the damaged area. This will protect the other tiles in the removal process.
2. To break off the tile you need a nail and a hammer. Position the nail in the middle of the damaged tile. Hitting the nail with a hammer will break the tiles and will detach them from the mortar.
3. Using a chisel and the hammer chip the mortar and rid all remnants of tile. Continue until the surface remains clean and even.
4. Keep your new tiles in water for a while. They will absorb water, which will increase their adhesion to mortar.
5. Start laying the tiles. Using a trowel spread a thin layer of mortar onto the back of each tile. Position the tile and press firmly. Make sure the tile is even with the existing tiled surface.
6. Allow 24 hours for mortar to dry.
7. Using a grout float apply the grout over the tile.
8. Scrub and wipe any grout excess with a wet sponge. Repeat the action several times until the tiled surface is perfectly clean.
9. Allow another 24 hours to grout to dry and your job is done.
Choosing Tiles for Your Bathroom | How To Build A House (howtobuildahouseblog.com)