Even if the parenthetical entry is authentic, I am not aware of any scripture that ever refers to unclean animals as food. Thus He could only be saying that clean animals would not be made unclean by eating with unwashed hands. However, as has been stated, the context of verses 1-20, has to do with the Pharisees practice of always washing their hands before eating. The subject is not clean and unclean animals, but unclean hands. The Messiah showed that unclean thoughts are the things that most defile a man, not just unwashed hands. After explaining that inner defilement of the mind is far worse than defilement of the body, the Messiah concluded: 19"For out of the heart proceed evil thoughts, murders, adulteries, fornications, thefts, false witness blasphemies. 20"These are the things which defile a man, but to eat with unwashed hands does not defile a man."
The Pharisees watched every word and movement that the Messiah made. They falsely accused Him of breaking the Sabbath, and claimed that He blasphemed when He said God was His Father John 5:18. But never did any Jew accuse the Messiah of eating, or advocating the eating of unclean animals.