I think this is really interesting, because it raises the questions of how much description you get from characters about their Moonlighting and Wealth. Especially with the Operator, I enjoy asking them a bit about the gigs they choose to work or not, what job it is they're trying to get done, so that if things go wrong we've got something to work with. I think this is in accordance with the principle, "to do it, do it."
Anyway, to bring this back to your question, if no time has passed then maybe devonapple's point remains. But if you feel like maybe some time has passed then let the Operator roll moonlighting, but if they say they want to work Honour as a gig, ask them how? what are they doing to regain their honour after the last session? If they can't come with anything plausible, then maybe they don't get to work that gig. And if they do come up with something that might work then awesome, let them roll! Either way, it stops being your problem.
I swear, half of the time when I have problems with AW, I can fix it by turning things back on the players and asking them to help make up the details that make the fiction make sense.