He doesn't like Gladio's anger much. That shouldn't come as a surprise. Dealing with pissy customers is a forte of his, but Gladio had maybe been kind-of-sort-of nice to him, so he's trying to extend a helping hand. It's frustrating, putting effort into something he knows he's bad at and having his efforts rebuked.

"It'll take me a moment." He takes the photo if it's being offered to him, and...he's still holding out the menu. "She hasn't clocked in yet, but I'll run--" Hah. Run. That requires legs. "--over to her place and ask her if it's that important to you."

He leaves the offer open. Someone who works at a diner next to an inn would certainly know all the comings and goings in town, right? Dylas wants to appear sympathetic, but Gladio's bad mood has spread to him, and instead he glowers like he always does.

"You can ask the innkeeper while I'm gone, right?"