When a Fae makes a promise in a bargain, he or she binds himself or herself to the promise. As we saw in Summer Knight, Harry had bound himself to Lea for three promises in exchange for whatever she gave him to fight Justine.. However Mab was able to take over that contract, then promises were then moved to her. In the case of Ethinu, Harry needed blood and had to say the right words to bind her, but she wasn't bound to Harry, she was bound to the prison.
Harry bound Ethniu. He beat her will to resist the binding. Not Demonreach. The prison is just where she is bound.
The Lady, Queen, and Mother mantles were already bound to behave under equal exchange. Harry did a favor for Winter, who were defending Chicago under their Accords, which the Fomor were attacking. Winter was obligated to return the favor. Harry demanded payment, they had no choice but to grant the favor or suffer the consequences, which we don't know what they would be. But, they would have to be serious.
When Mab acquired Harry's favor to Lea, we don't know how. Did Mab demand them as service from her vassal? Was it the price Mab extracted to cure Lea of Nemfection? Or did Mab trade a favor to Lea in exchange for Harry's favor? While Lea was incapacitated by being cured, Mab acted to fulfill her vassal's obligations. Just as when Harry was mostly dead Mab acted to fulfill his obligation to train Molly, transferring that obligation to Lea, who was already bound to fulfill Harry's obligation to train Molly as his Godmother.
Harry himself has a ton of obligations. And not just favors owed to others. He is owed favors and tends to forget them or brush them off. I'll be watching to see if he doesn't start taking those favors owed more seriously as the mantle takes hold.