NURSE: No, you cannot hit me.
LORELAI: Can I bite you or pull your hair or use the Epilady on you, ’cause I really need to do something?
Epilady was the brand name of the first epilator, an electrical device used to remove hair by mechanically grasping multiple hairs simultaneously and pulling them out. It was released in Israel in 1986, manufactured by Mepro on a kibbutz.
They were notoriously painful to use, sometimes likened to torture devices, so Lorelai thinks of it as something painful she can use on the nurse to take her mind off her labour pains, like biting her or pulling her hair.
Obviously this flashback can’t have actually happened, because it is October 1984, and the Epilady hadn’t been invented yet. Perhaps it is a false memory. (If so, can we really trust any of the flashbacks?).
The Annotated Gilmore Girls 