Have you heard of the phrase this one first then you? It's never fun being put second. Jesus told this woman, "Let the children be filled first. For it is not good to take the children's bread and throw it to little dogs". This woman recognized Jesus being Lord and she sought grace not entitlement/due that the children of Israel seemed to have. Even though she knew she was not deserving to sit at the table, she was happy to have the fallen crumbs under the table.