7:1-23 Ritual purity isn’t so important. More important is actual moral purity. “Am I being a pharisee?”
Incidentally, the “corban” thing, some time after Jesus, the rabbis actually decided Jesus was correct about this point.
7:24-30 The Syrophoenician woman: In one of the movies made about Jesus, they showed this as Jesus the human learning from the experience in overcoming the Jewish prejudice he grew up with. Many Christians balk at this interpretation because “Jesus was perfect! How could he have had racism?” but Luke 2:52 said that Jesus did grow in wisdom. So I dunno.
But as far as application goes, we can use this to ask ourselves, “What prejudices do I have that I need to grow from?”
7:21-27 Jesus now goes to the Decapolis and healed people, but this time he told people not to tell anyone. Interesting -- change since the time of the demoniac.