If you were to "salvage" a U.S. Navy Submarine with nukes, the U.S. government would, without doubt, either "seize" or destroy it.
Even if you were going to use it to save the world.
So why is it that James Holden and his crew were able to salvage an MCRN frigate with nukes, with little to no consequences?
Isn't the Martian Government bothered that its ship is being used for what ever by a bunch of civilian foreigners, or don't they have the means to "get it back"?
It has been captured under the "law of salvage":
This has been addressed in the show and in the books - by the law of salvage, whoever claims abandoned vessel in space has the right to keep it. Of course, Mars wasn't too happy about it, but it cannot act with force, as this will further destabilise the political situation within the system.
In the book Mars sues Holden, but the case is dropped soon after. Or to be more precise: in the "Abaddon's Gate" Mars sues Holden asking for the return of the "stolen Tachi". The ship is impounded, but the "friendly" news company decides to step in and help Holden if he will allow journalists on board of the Rocinante and go to the Ring.
He paged through the summons, jumping past seven pages of legalese to get to the point: The Martians wanted their ship back. Official proceedings had been started against him in both Earth and Martian courts challenging the salvage claim to the Rocinante. Only they were calling it the Tachi. [...]
If they took the case before a magistrate, they might or might not lose the ship, but it would be expensive to find out. Accounts that Holden had thought of as comfortably full suddenly looked an order of magnitude too small. [...]
“You’re sure you can get the hold taken off the Roci?” Naomi asked.
“I am protected by the Freedom of Journalism Act. I have the right to the reasonable use of hired materials and personnel in the pursuit of a story. Otherwise, anyone could stop any story they didn’t like by malicious use of injunctions like the one on the Roci. I have a backdated contract that says I hired you a month ago, before I arrived at Ceres. I have a team of lawyers ten benches deep who can drown anyone that objects in enough paperwork to last a lifetime.”