Or, if they had killed Kurn, they could've gone back in time and "unkilled" him. No - Kurn was dead, even if his body wasn't. Why try to undo what had happened?
Because that's what Worf does about his Honor throughout most of his existence in the franchise. He tries to undo what had happened.
Uh, no he doesn't.
When Worf was discommendated by K'Mpec, he didn't do anything to regain his honor. He got it back because he supported Gowron, who gave it back to him. Then Gowron stripped his honor again, and Worf didn't fight it. He joined the House of Martok, but the House of Mogh was ended. I suppose Worf's personal honor was restored by joining an honorable House, but really the point is that the House of Mogh was dead. Why try to bring back Kurn, then? He was as dead as his House.