Some TMNT stuff really isn't for little kids.
Oroku Karai is a high-ranking ninja of the Foot Clan, as well as being the daughter of the Shredder. When her father was imprisoned on Rikers Island, the Foot Clan split into multiple factions, and Karai was challenged for leadership by the Foot Elite. The Turtles intervened when she was attacked by them on a train car, allowing her to escape.
However, a bigger threat arose in the form of Bane, a monstrous criminal from another dimension. After the Turtles failed to stop Bane and his Venom-enhanced forces, Karai was informed by the few loyal ninja she had left that Bane had no secret base, and that his headquarters was on Liberty Island.
She and her men went there disguised as ordinary civilians, and when Donatello's gas flushed the Venom from Bane's Foot ninja, they began fighting to reclaim the clan. She fought alongside Batgirl as her father fought Bane himself with Batman and Splinter. Shredder commanded the Foot to go to Karai, and they obeyed, ending the immediate threat of the fractured ninja clan.
- While similar in most regards to her IDW counterpart, as most of the characters from the Turtles' dimension are, Karai refers to herself as the Shredder's daughter and not his granddaughter. Their exact relationship is not elaborated upon.