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Genevieve Parker was the wife of Wendell Parker, the mother of Danny Parker, the grand-mother of Danny Parker Jr. the great grand-mother of Jennifer Parker.
In 1875, Thaddeus Tannen captured Wendell and Genevieve, and tied the latter to the train tracks. Tannen threatened to keep her there until the train arrived, which forced Wendell to sign over their ranch to the Tannen family.
These events were changed when Marty, Jules and Verne arrived in the Time Train. Marty successfully interfered with events by giving Tannen a pen full of ink that would fade over time, meaning that the Parker family of the 1990s would still own the ranch.
Thaddeus left without untying the Parkers, but luckily they were freed by Verne before the train ran them over. It is unknown how Genevieve and Wendell survived in the original timeline.