The pictures are not nearly as bad as I thought when I was reading your post. I would see a vet about treating this. Good luck with this splendid frog.
I wouldn't be too hard on the mother of your daughter's friend, as she actually rescued this frog from becoming someone's meal. The Chinese food markets are animal lover's nightmare. I have never been to one but I have heard the tales and have seen the video. It angers me every time I think about it. Live animals are stacked in crates like potatoes, with the poor souls on the bottom being crushed to death. There are no refrigeration units to speak of, so often animals are butchered alive, having pieces of their flesh cut from them. An agonizing way to die.
For those unfamiliar with the species, Hoplobatrachus rugulosus or Chinese edible frog is a semi-aquatic Ranid similar to the North American bullfrog, Lithobates catesbeianus. It is a native to Cambodia, China, Hong Kong, Laos, Myanmar (Burma), Taiwan, Thailand, and Vietnam. It has also been introduced to Malaysia. Its IUCN (Red List) status is Least Concern.