You've got a number of potential issues.
1/ The compatibility of the tile with underfloor heating, has this been confirmed with the manufacturer as much of this quartz has a habit of curling up at the edges when the heating is run?
2/ Lets assume there is a company that can grind and refinish this stuff to a decent degree, when you reduce the thickness of the tile even by 2mm or 3mm it increases the prospect of point 1 occurring.
3/ Once you start trying to rectify it becomes your problem.
So as it's only 60m2 so far, suggest they pull it up and fit it correctly. Having first checked it can be used with UFH.