Relieve the grout around the offending tile with a "hand grout saw" being very careful not to go deeper than the thickness of the tile.
Then use a hammer to pulverize the tile. Don't get too aggressive. Once the tile is broken begin to remove the rubble again not going below the thinset substrate.
Then use a rub stone to grind away the thinset under the tile to the point that it all began and a new tile will properly fit the opening.
What was the mat imbedded in to begin with? Was it thinset or SLC?
