It is noteworthy that while in Matthew and Mark the surrender to the Jewish authorities is mentioned first, and afterwards the surrender to the Gentiles, in Luke this latter alone is mentioned. Luke certainly presents generally a younger form than Mark, but occasionally, it would seem, an older, which need not surprise us. I suspect that the oldest thought was of the surrender of the great Idea of the Jesus, of the Jesus-cult, by the Jews to the heathen. This, in fact, was the supreme, the astounding, fact of early Christian history, and engaged intensely the minds of men.
(Ecce Deus, p. 312, my bold)
It would seem that Mark is judaizing here: Jesus is given like a gift package to the Gentiles only after that he has been given like a gift package to the Jews. The passage through the Jews is designed to mean that the Salvation comes from Jews, as an act of due filtering.