A.T. Robertson Commentary Mark 7:26

"Now the woman was a Greek, a Syrophoenician by race. And she besought him that he would cast forth the demon out of her daughter." — Mark 7:26 (ASV)

A Greek, a Syro-Phoenician by race (Hελληνισ, Συροφοινικισσα τω γενε). "A Greek in religion, a Syrian in tongue, a Phoenician in race" (Bruce), from Euthymius Zigabenus. She was not a Phoenician of Carthage.

She besought (ηρωτα). Imperfect tense. She kept at it. This verb, as in late Greek, is here used for a request, not a mere question. Abundant examples in the papyri in this sense.