Physicians of nineteenth century America used papaya leaf to treat "fermentative indigestion," a condition of bloating, nausea, and flatulence frequently following eating too much fermented foods. King's Dispensatory is quoted that the teas (decoctions) of papaya leaf helped reduce the oxalic acid content of the urine, presumably reducing the formation of oxalic acid kidney stones.
The primary use of papaya leaf for herbalists today is as a vermifuge, that is, to remove intestinal worms. Papaya leaf has less of the protein-dissolving papain than the fruit, so it is less likely to "dissolve" the worms, but it contains tannins that the fruit doesn't. These tannins protect the intestine from reinfection by "tanning" proteins in the lining of the intestinal wall so that worms cannot attach themselves. Neat huh?