Mat 15:22 And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, thou Son of David; my daughter is grievously vexed with a devil.
Mat 15:23 But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us.
Mat 15:24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
Mat 15:25 Then came she and worshipped him, saying, Lord, help me.
Mat 15:26 But he answered and said, It is not meet to take the children's bread, and to cast it to dogs.
Mat 15:27 And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters' table.
Mat 15:28 Then Jesus answered and said unto her, O woman, great is thy faith: be it unto thee even as thou wilt. And her daughter was made whole from that very hour.
Luk 16:21 And desiring to be fed with the crumbs which fell from the rich man's table: moreover the dogs came and licked his sores.
The "Jews" called Gentiles dogs. It didn't matter whether you were of the lost sheep of the House of Israel (ten tribes?) or a Caananite or some other origin. I think Jesus was making two points in the above verses, He was sent to bring the House of Israel back into His coming Kingdom, but God has always taken in to the "fold" anyone who wants to follow the God of Israel.