Interesting ethical question, sort of mirroring a discussion I was having about the Punisher on another forum yesterday.

His spirit is pure, from (as a certain Jedi put it) a certain point of view. He's never denied his actions, even to himself, he is always entirely open and honest about his mission and his intentions. He's a killer certainly but has never preteneded to be anything else.

What he's not is GOOD, but I'm not sure the Eye cares about that part of your alignment.