>Sometimes when a leo sheds, there toes dont loose all the skin and it can get caught. It sounds to me liek this has led to an infection.
WiteLeo is right, its probably from a bad shed, and now its infected. the green color sounds like bacterial infection.
BUT DONT SNIP THE TOE OFF! (*smacks WiteLeo!) Put Neosporin on it every day or twice a day until the scab falls off and ther toe end shows clean healed skin. The gecko might lose the toe tip but the Neosporin will (should) cure the infection and keep the loss to a minimum.
And about the eating, she might be still getting used to her new surroundings. If she doesnt start eating in a few days, or if she is already thin or has a thin tail right now, then she could be sick.