Theophylact of Ohrid — as excerpted in the Catena Aurea on Mark 7:24-30

“He calls the Gentiles dogs, as being thought wicked by the Jews; and He means by bread, the benefit which the Lord promised to the children, that is, to the Jews. The sense therefore is, that it is not right for the Gentiles first to be partakers of the benefit, promised principally to the Jews. The reason, therefore, why the Lord does not immediately hear, but delays His grace, is, that He may also shew that the faith of the woman was firm, and that we may learn not at once to grow weary in prayer, but to continue earnest till we obtain.”