Here's a suggestion. Get some Poultry Nutri-drench. For whatever reason, this hen may be suffering from a nutritional deficiency. This supplement will give her an immediate boost.
Chickens pick at their feet when the feet are causing discomfort. You may not recognize what scales infested with mites look like, but that is what I suspect some of her problem may be. The treatment is very simple and need not even cost you anything. If you have castor oil, Vaseline, coconut oil, even Crisco, you have the treatment for scaly leg mite. Just smear on the oil over all the scales, including bottoms of feet, between toes, and legs all the way up the shanks.
While you are handling her, inspect the bare skin around her vent area and see if there may be some creepy-crawlies. Lice are common tenants on chickens and can make them feel miserable. The treatment is cheap and simple by picking up some permetrin poultry dusting powder.
Lastly, check your coop after dark with a flashlight. Look to see if there are mites on the roosting perches crawling up the legs of your chickens. You may need to treat the premises for mites.