Who were the exceptions to Jesus' Israel-only ministry in the Gospels?

Les explains that Jesus chose the Twelve in Galilee and commanded them in Matthew 10 not to go into the way of the Gentiles or into any city of the Samaritans, but rather to the lost sheep of the house of Israel. He notes that throughout His three years of earthly ministry, Jesus Himself confined His ministry only to Israel, with two exceptions: the Roman centurion and the Canaanite woman. The Canaanite woman was at first even ignored, and the Twelve said to send her away because she was a Gentile. Les says this is not a contradiction; it is a change of program. Later, after Israel is set aside, God goes to the Gentiles, and Paul can write of obedience to the faith among all nations, not just Israel.