Jamieson, Fausset and Brown on Leviticus 22:15-16

15-16. they shall not profane the holy things of the children of Israel--There is some difficulty felt in determining to whom "they" refers. The subject of the preceding context being occupied about the priests, it is supposed by some that this relates to them also; and the meaning then is that the whole people would incur guilt through the fault of the priests, if they should defile the sacred offerings, which they would have done had they presented them while under any defilement [Calvin]. According to others, "the children of Israel" is the nominative in the sentence; which thus signifies, the children of Israel shall not profane or defile their offerings, by touching them or reserving any part of them, lest they incur the guilt of eating what is divinely appointed to the priests alone [Calmet].