Chop one in half and you will see a pithy core surrounded by up to 200 small seeds (smaller than sunflower seeds) that are much sought-after by squirrels. Try to harvest these seeds for yourself and you will get a clear understanding of how much the squirrels must like them! In addition to ripping apart the tough, stringy fruit, there is a slimy husk around each individual seed that must also be removed before the seed can be eaten. Nonetheless, Osage Orange trees are a magnet for every squirrel in the neighborhood. They typically sit on the ground at the base of the tree or on a wide branch up in the tree to disassemble their prize, making a big mess in the process. Piles of shredded hedge apple are a sure sign of squirrels in the area.