What does Matthew 15:31 mean?

What ancient Israelites would have considered "mountains," many other cultures would consider very large hills. Christ is not scaling a rock face; He's in a place where people can walk to where He's positioned. This spot is in the mostly-Gentile region of the Decapolis, literally meaning "ten cities." Here, on the southeast side of the Sea of Galilee, crowds of people bring their sick and afflicted.

Jesus is healing these Gentiles without any of the reservations He expressed to the Canaanite woman in the previous section of verses (Matthew 15:21–28). That makes it even more likely that His interaction with her was a deliberate teaching moment for the disciples. What Israel has mostly ignored, the Gentile world will come to embrace (Romans 9:30–33).

In fact, Jesus seems eager to provoke these Gentiles into glorifying the God of Israel. Matthew says the people wondered when they saw their friends and neighbors healed. The mute spoke. The lame walked. The blind saw. Crippled people became healthy. Perhaps some in that area knew that these miracles were to be signs of the coming of Israel's Messiah (Matthew 11:2–6; Luke 7:18–23). If so, that was even more reason to give God glory.