When I enlarge the photos, it looks like both birds are having problems with their toes. I'm not familiar with what might be going on with them, it doesn't look like scaly leg mites. Do you have access to an avian vet, who could take a scraping of the toes to see if it is some kind of mite?
I agree with the others, a seed-only diet is not sufficient nor healthy for our finches. Egg food, which can be as simple as a mashed hard-boiled egg, is full of protein and many vitamins. Veggies, especially dark greens (kale, broccoli, etc) provide more vitamins too. In the wild, most finches eat plants and insects in addition to their seeds, so we need to give them a varied diet as much as possible. I'm assuming they also get a mineral supplement, which can be as simple as oystershell grit.
Welcome to the forum! There's lots of good reading at
www.finchinfo.com, where you will find many articles on finch care, especially nutrition. If you put your general location in your profile, it makes it easier to answer locale-specific questions later on.