Final answer:
Sarah Winnemucca convinced President Hayes to allow the Paiute Indians to return to their homelands through her activism and lectures in the 1880s.
Step-by-step explanation:
The individual who convinced President Hayes to allow the Paiute Indians to return to their homelands was Sarah Winnemucca. A member of the Paiute tribe, Sarah Winnemucca was an activist who lectured throughout the East in the 1880s, working to inform White audiences about the injustices faced by Western tribes.
Her relentless campaign eventually aided in the return of her people to their native lands. The activism of Winnemucca and others helped pave the way for later reforms, such as the Indian Citizenship Act of 1924 and the Indian Reorganization Act of 1934, which aimed to restore rights and self-governance to Native American tribes.