Theologically, this woman's faith is incredible. This woman is saying that she knows that Jesus belongs to the Jews. But she is also saying that if she can have even the crumbs, the tiniest piece of Jesus, that would be infinitely more than she has now. Even the smallest crumb, rejected by someone else (a crumb on the floor), would satisfy her need. She had enough faith to know that anything that Jesus would throw her way, no matter how small, would help her daughter.
