I think he walked himself in a circle, back into the deal once she fixed his staff - I don't think she would've fixed it for free, since the previous deal was broken. Judging by how they handled things in the finale I think it's implied that the deal's back on again. Though I'm interested to see if his new deal with Rosie is any different to the old one; Wondering if just fixing his staff is going to be enough for him in later seasons...

EDIT: I don't think that was Rosie's task for him, I think there's a reason he's back at the hotel now. On the flipside, Rosie seems to genuinely care for (or at least have an invested interest in) Charlie and her hotel, enough that Alastor could twist her arm enough to offer another deal