Or HaChaim on Exodus 29:33/אור החיים על שמות כ״ט:ל״ג

1 ואכלו אותם אשר כפר בהם, "and they will eat them with which atonement was made." They will eat those parts of the animal in their capacity as owners and not in their capacity as priests. The meaning of the words אשר כפר בהם is that the consumption of meat of the peace-offerings by their owners confers atonement upon them. Even Moses was forbidden to eat of any of these parts of the animal, though he was permitted to eat the breast and the thigh.