Take a hammer, whack it hard in the middle to break it, take the pieces out and put in a new tile. If you are really lucky (depends on how old the thinset is, you might get it up, but would likely crack an adjacent tile in the process, so best to just sacrifice that tile.
Grout helps stabilize the tile, protects the edges, and helps to keep crud from getting down between the tiles, but isn't designed to hold them down or support them on the bottom. Grout can also make a design statement.
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