Giving the dog a crumb doesnt save the dog. She has no spirit from above. He told her to go away because He didnt come for her. God has limitless power. If He wishes to grant Her an earthly request, He can do so. Even the demons know God is one, bit that wont sage them on judgment day. You want to see something that isnt there. There are unlimited examples of this.

John 10 you do not believe me because you are not my sheep.
They are not and can never be His sheep.