My read:
He stared at sudden, assumedly beautiful, "Thank you" smile, covered it up with his classic amused look, then LQ kept looking at him to find more sincere feelings, and he looked away because maybe he has them and is bashful.
A cute moment, in the also negotiating a snitch agreement to avoid explosive international fallout way.
More than a little bit manipulative on LQ's part, though, and if LQ has feelings to return for him, her "continued observation" moment is where I'd expect to hear a snip of them, since we're in her head. Silent as it is, it's hollow like she's waiting to feel something, and we get *his* reaction breaking eye contact.