Season 3 of the TV show clearly indicates that the Mars government want their gunship back - and quite understandably so. That never gets resolved in season 3 because it’s basically introduced as an on-screen excuse for the presence of the interviewers and, anyway in-universe there is no time to argue about it with everything that happens.
Season 4 is mum about the subject. Months have passed since Season 3; Holden has an open meeting with the UN Secretary-General while the Rocinante somehow gets a rail gun (!) installed (there’s a “Chekhov’s gun” if I ever saw one) which implies at least Earth (possibly all three governments) accept the status quo. It also means that someone is willing to openly furnish the team with expensive top military-grade weaponry presumably at no cost. Obviously these guys are not hiding in the belt keeping their heads low.
For the purpose of this question I’m not looking for any event that might or might not happen after the Cibola Burn events.
The question: Do the books (or other media) address the subject of legal ownership/control of the Rocinante/Tachi at all? Has Mars given up their claim to the ship (again, at this point in the storyline)?
(One has to wonder what the official status of the team is, in the eyes of the three governments; but that would require a separate question)