He can tell she's very on-edge, which is... To be expected. He won't expect her full trust right away, he's patient.

But at her admission, his brow furrows, an exhale of slight shock escaping him. That's a very deep level of distrust. He frowns in concern- he doesn't want any Visitor sleeping rough, least of all someone who's already had things so rough. Especially in winter!

"You're welcome to crash with me. Or, if you prefer your own spot, there's a little abandoned shack on the beach, which I used to live in. Nothing fancy, but free for the taking."