Did Wittgenstein influence Austin's philosophy of language, and, if so, when and how?
We don't think so! Neither did Grice.
There are currently two schools of thought, both of which are problematic. First, many assume without evidence argument that Austin's work was heavily influenced by Wittgenstein. Second, many of Austin's colleagues and students claim that Austin's work developed independently of Wittgenstein.
Grice draws on textual evidence to argue that Austin's work on language was influenced, at all stages of its development, by engagement with Wittgenstein's ideas.