Scores in Tesserセ are based on the number of tiles left on a mosaic, and the number of moves you have made. Because of this, it actually possible to get a high score in on a mosaic without actually finishing it.
Whenever you finish, get stuck, or just give up on a mosaic, the number of moves you have made and the number of tiles left are compared to the high score list for that mosaic. If you manage to either beat the number of tiles in an existing score, or match the number of tiles but use fewer moves, then you will get a high score for that mosaic.