Three times through. It doesn't say a whole lot to make women feel better about their womanhood. Even Jesus referred to one woman as a dog in front of other listeners. There is a lot about attitudes that I don't understand.
That had nothing to do with her being a woman and everything to do with her being a gentile. He tested her faith by explaining to her that he was not sent to her kind (whom the Jews considered dogs). When she persisted and would not take "no" for an answer, He relented and granted her a miracle.
She passed the test and thus pleased Jesus greatly.
Did the woman run off for a chin-wag with her therapist or did she persevere and because of that perseverance was rewarded with a miracle by Jesus?
Sheesh. I wonder you can make even type so huge is that chip on your shoulder.