If the Field Operative has a block on their card from their special ability, what happens to that block if they were to play New Assignment?
The blocks are returned the supply.
It's a niche scenario that's not really covered in the rules
The rules do say
The Field Operative may return sample cubes from his role card back to the supply at any time
Which is beneficial if the supply is about to run out and you can prevent a loss by returning cubes to the supply. In the case for this question it does allow the return of the cubes.
There's no advantage for the players to the cubes being put back into the supply - the action to gather the cube has already been spent, and is equivalent to a "Treat" action for any other role. You lose out on getting the potentially easier cure though.