Oroku Nagi was a member of the Foot Clan who was a rival to Hamato Yoshi. Among the things he was rival to Yoshi in, was the love of a woman named Tang Shen. Shen loved only Yoshi, though, and when she set the record straight, Nagi flew into a rage and began to beat her. Yoshi arrived in time to intervene and slew Nagi, then fled to New York City with Shen out of dishonor. However, they were eventually followed by Nagi's younger brother, Oroku Saki, and both Yoshi and Shen were killed.
The existence of Nagi in Splinter's flashback is one of many minor yet significant differences between the comic adaptions of the films and the films themselves.