If he comes square off the back wall chances are the tiles will be short to the furthest point away on the door wall So something has to give.
The biggest mistake the tiler made was not to involve you in the set out......However that's not always possible.
Taking them up is just going to remove this visual "mistake" and create another, it is running visually square to the door wall and once you've filled the brick wall side up with your sanitry stuff it's not going to look out of square as much. Your room is definitely out of square without a doubt, I personally would have set out differently with it being square but everyone is different! I think it's a mistake pulling them up to move it around 30mm or so as this will make the doorway look out by quite a bit and that's going to be a bigger eye sore and look like a real mess up!
To your question though, your boards should be fine if you make the tiler take the tiles up.