I understand that it may be possible to move this (non functioning) button without a trace if the fabric is pressed afterwards (it's wool), but how does it look as is? Had to get it extended by an inch.
I would return to the tailor who performed this alteration and insist that he / she correct this. There shouldn't be an issue with removing faux button holes on a wool garment.
I would then find another tailor that doesn't take short cuts!