Who has a hurt expression in "He looked at her with a hurt expression"?
Solution 1:
The writer, by writing that he looked at her, implies that his expression might be relevant. So this would fit in with the writer saying, in the same clause, that he had a hurt expression.
A point of grammar also supports this: "with a hurt expression" is an adverbial phrase which may naturally modify the verb "looked". But admittedly this is not completely compelling evidence, because in another context that same phrase might modify a noun, e.g. "Looking around the room, he spotted a woman with a hurt expression".
But it's not possible to say this with complete confidence, given only that one sentence. Some additional context might make the matter clearer.