Jesus' program is for everyone; beginning with the lost sheep of the house of Israel and extending to everyone. His program is to everyone who will come to him by faith, as can be seen in the passage you just cited...
Matthew
15:24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
15:25 Then came she and worshipped him, saying, Lord, help me.
15:26 But he answered and said, It is not meet to take the children's bread, and to cast [it] to dogs.
15:27 And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters' table.
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.
This was the program the whole time; "The just shall live by faith." No exceptions.