Actually, when the bird is freshly killed you can literally rip the feathers off, and completely remove the breast meat with your fingers. No marks whatsoever.

Same is true for a large bird of prey, they can use their beak and have almost 100% success of removing the breast, leaving nary a telltale sign.

Most terrestrial predators will also eat the bones, especially bobcats and coyotes. They very seldom leave the bones, but will leave the feathers.