Some TMNT stuff was always meant for grownups.
Karai is the former head of the Japanese branch of the Foot Clan. When her daughter Amai was rendered comatose and suffered brain death during City at War, Karai quit the Foot to care for her. However, she also had been secretly having the New York Foot Clan members killed as revenge for their attempted killings of herself as well as Amai.
In TMNT: Urban Legends #24, Leonardo, Raphael, and Pimiko track down Karai, as they believe she is the mysterious Lady Shredder. Leo breaks in through her window to find her sitting by Amai's side, and explains that not only is she not Lady Shredder due to abandoning the Clan, but she also detested Oroku Saki and his "Shredder" mantle.
Not long after, Pimiko and Raph swung into the room, and Karai mocked the spawn of Saki by calling her unloved and unwanted. Pimiko attempted attacking her with a katana, but Karai knocked it from her hand even in her sitting position, and turned it on her before handing it back. She told the kunoichi that she should listen to someone she's known most of her life if not her, and suddenly, Go-Komodo and Lady Shredder appear.
Komodo says that Pimiko was the product of the union of his sister, Kujikiri, and Oroku Saki. Kujikiri was once a kunoichi allied with him, but she became an assassin for hire on her own, calling herself Headhunter. She met Saki when on a job to kill him, but ended up having a secret affair with him. When Pimiko was born, Kujikiri dropped her off with her brother to be raised.
As Pimiko fights Komodo and Leo faces Lady Shredder, Raph confronts Karai about killing a score of Foot Clan members. She explains why she did and and Raph argues that they could have worked together, but she counters that his own men flipped on him as soon as the Japanese branch showed up. Raph claims that they wouldn't have if not for the turncoat Cheng, and Karai tells him he need not worry about Cheng any longer.