I’m not sure what the material is behind the tile, and it could be that the surface isn’t meant for tile. To me, though, it looks like there wasn’t enough thinset applied during the install.
Typically, you would need to clean off all the old thinset from the backer surface and the tile. Then you would need to apply thinset again with a trowel. Probably a 3/8 square trowel application for that size tile? Push the tile back into place, making sure it sticks in there. Clean out any thinset from your grout lines.
It’s very difficult to match grout though. Do you have the original?
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