Having read the book, Vengeance, I will tell you that the character had no ambivalence about his job but in the end he thought that it didn't do anything to stop terrorism.
During the first hit there was some hesitation but only for a moment. To take a life in the form of an assassination should give someone a second to pause...
but only a second.
I read the book as well.
Avner's (the main character) problem was the way in which he and his team was treated by their Mossed handlers after the job was done.
He had no issue whatsoever with the killing of the terrorists.
I have not seen the movie, but if it portrays the team as remorseful in any way, they got it wrong, very wrong...