Hank would assure him that feeling pain for others is a part of empathy. It's not that he has no right to it, but rather an understanding of where their pain might be coming from. Connor is an empathetic being; he's allowed to feel for other people. It's a motivator to help them.

"Yeah, well. You'd be the best one there." Is what he ends up saying, putting his free hand on Connor's shoulder as he takes a drink.

"Do you wanna get out of here?" He puts down his near-empty mug then, and wipes his mouth with the back of his hand.