In Season 3, Episode 7, Why does Lord Bolton send Jaime Lannister back to King’s Landing, instead of sending him back to Robb Stark?
SPOILERS BEYOND THIS POINT
The existing answer is correct albeit lacking in details.
There are two chief reasons for it:
- "Lannisters always pay their debts"
- Selling Wolf pelt for lion skin
Lannisters always pay their debts
There is a famous saying in Westeros that Lannisters always pay their debts. It is both a symbol of trust on words of a Lannister and also a promise of retribution to their foes.
Robb Stark was himself aware of how deeply it was embedded in Westerosi mindset, therefore he was reluctant to let Jaime stay with any of his bannermen.
From Season 2 Episode 1:
Jaime: King in the North! I keep expecting you to leave me in one castle or another for safekeeping, but you drag me along from camp to camp. Have you grown fond of me, Stark? Is that it? I've never seen you with a girl.
Robb: If I left you with one of my bannermen, your father would know within a fortnight and my bannerman would receive a raven with a message: "Release my son and you'll be rich beyond your dreams. Refuse and your house will be destroyed, root and stem."
Jaime: You don't trust the loyalty of the men following you into battle?
Robb: Oh, I trust them with my life, just not with yours.
Roose Bolton was aware of that as well. He knew that Casterly Rock's retribution for Jaime's maiming would be swift and dire. He also knew that his cooperation in Jaime's release might however see him a rich man until his death. But he wasn't sure that if releasing Jaime would be enough to make Tywin Lannister to wipe the slate clean. This is why Roose Bolton asked Jaime to supper and had following conversation with him:
Bolton: I should send you back to Robb Stark.
Jaime: You should. But instead, you're sitting here watching me fail at dinner. Why might that be?
Bolton: Wars cost money. Many people would pay a great deal for you.
Jaime: We both know who would pay the most. Or make you pay the most if he found out you had captured me and sent me back up north for a summary execution.
Bolton: You're right. Perhaps the safest thing to do is to kill you both and burn your bodies.
Jaime: It would be, if you honestly believed my father would never find out about it.
Bolton: King Robb is keeping your father quite busy. He doesn't have time for anything else.
Jaime: He'll make time for you.
Bolton: As soon as you're well enough to travel, I will allow you to go to King's Landing as restitution for the mistakes my soldiers made. And you will swear to tell your father the truth, that I had nothing to do with your maiming.
As you can see, it was a proof and gesture of good will by Roose Bolton, to prove that he had nothing to do with Jaime's maiming. Doing that, he was hoping that he would save himself from Tywin Lannister.
Lion's skin instead of a Wolf's pelt
By that time, the following events had occurred:
- Robb married Talissa Maegyr instead of a Frey girl as he promised, resulting in break-down of his alliance with the Powerful lord Frey
- Execution of Lord Rickard Karstark, which lead to desertion of Karstark levies
- Battle of Duskendale, where most of Robb's infantry got slaughtered. (Even though that battle happened because of Roose Bolton's treachery and had nothing to do with making up his mind since he had already decided).
- Battle of Blackwater and Lannister victory against Stannis.
- Alliance of Tyrells and Lannisters with marriage of Margaery and Joffrey.
- Alliance of Martells and Lannisters with betrothal of Myrcella and Trystane.
- Occupation of the North by Greyjoys
- Death of Bran and Rickon, Robb's heirs.
It was clear in light of these events that victory of Starks was impossible and a total Lannister victory was inevitable with every passing day.
Walder Frey and Roose Bolton both reached the same conclusion and they wanted to be on the right side when all this was over. So they got into negotiations with Tywin Lannister. Of course a major requirement in any possible alliance between the Boltons and Lannisters was immediate release of Jaime Lannister however Roose wasn't sure if it was gonna work out as he planned when Tywin Lannister finds out his golden son has been crippled. That is why Roose decided to meet with Jaime, man to man and ask him to tell his father that he had nothing to do with the maiming. He again said that before bidding Jaime farewell in Season 3 Episode 7:
Bolton: You will give my regards to Lord Tywin, I trust?
Jaime: Tell Robb Stark I'm sorry I couldn't make his uncle's wedding. The Lannisters send their regards.
He wanted to stay in good with the Lannisters (with Joffrey on the throne, Tywin Lannister was literally in charge) as he was sure that they would win the war between the North and the current crown. Rob Stark had become weaker as he had lost the Freys and the Karstarks as allies. Lord Bolton was also getting frustrated with Rob as Rob's attention to the war at hand was being taken by his new love Talisa.
Also when talking to Walder Frey,
He ignored my advise at every turn, if he had been a trifle less arrogant
By freeing Jamie, it meant he was at least willing to be an ally to the Lannisters when push came to shove as ended getting the North for himself.