[he sees Illya all but shutting down and feels like he hasn't quite managed to help her. But he's also not sure how to continue pursuing it when she's all but made it clear that she doesn't want to continue]

...

I'll go and ask the museum staff to see if we can meet up with the diorama maker. [he smiles a little helplessly at her, clearly worried but trying to respect her boundaries too] Do you want to exchange contact information? It might be easier to coordinate that way.

[it's just a formality. He'll wave Illya off once they've arranged something]

You probably need to get back to the ice cream stall... Take care of yourself, Illya-chan. I'll see you next time.