Theia Mania

I don’t know the exact methods of purification in ancient Greece, but "among agents of purification, the most widely used and most basic was water. Particular springs were especially favoured for purifications, and the most prized cathartic water was that of the salt-stained sea" (Miasma: Pollution and Purification in early Greek Religion by Robert Parker). If Hekate and Persephone had been humans, the purification would also have included sacrifices to certain gods.