Maybe not right now but he'd definitely kill him when he returns to the future. Whenever that is. Does he have to go back? Probably.

"Huh? Oh. You can't-I mean I'm supposed to-uh-I kinda really, really messed up in future? Or Recently-or whatever and Fury sent me back to find records on someone because we're pretty sure he used to work for you? But he definitely destroyed all record of that. Or he will-I wonder if he got blipped." He says the last more to himself than to Tony as he follows after him.