Jesus and Gentiles

Matthew 15:21-31 confuses me.

Jesus says He isn't sent to any people except Israel (vs 24).
But then He goes to the Decapolis, a pre-dominantly Gentile region (vs 29) and heals many there.

Huh?

My best guess is that Jesus was testing the woman in vss 22-26, to see just how "poor in spirit" she really was. After all, God says it's too small a thing to just go to Israel - He's going to send His Messiah to be a light to the Gentiles, too (Isa 49:6).

But the woman apparently knows Israel's history quite well and places herself within it, as an outcast not deserving grace (2 Samuel 9:8-10).

Paul seems to be following his Master when he says salvation is to the Jew first and also for the Greek (Rom 1:16-17). Jesus doesn't gloss over that salvation is of the Jews (John 4:22). He is the Jew we Gentiles cling to for salvation (Zech 8:23).