Burnham does that old Trek standby of disobeying orders to go on a mission of personal importance. We get Georgiou being snotty, action, adventure, a prison break, self-sealing stembolts, and a heroic sacrifice. Plus back on Discovery, Stamets and Adira bond, Saru has a crisis of captaincy, and more Grudge the cat!!!!! My review of Star Trek: Discovery‘s “Scavengers.”
Speaking of Georgiou, her presence on Discovery is now, as I said at the start, extremely problematic. I actually had no issue with her being on board, and even being allowed to roam freely, when they first arrived in the future. There’s no use in antagonizing her, as it will just pit her against everyone on board, and she’s not someone you want on the opposite side of a fight. By giving her a certain amount of free rein, Saru is able to make use of her (e.g., to get rescued from being held at gunpoint) without pissing her off and setting her against him.
But it’s not clear why Vance is seemingly okay with the deposed fascist running around freely on a Starfleet ship. Saru not throwing her in the brig when they were timelost and alone made sense—a brig is a holding cell for when you bring someone to a proper authority, and they had no proper authority. Now that they’ve found Starfleet HQ, though, why is she still there?