Picking up on Codex24's insight, but taking it in a different direction:
It's John, not Mark, who takes the conversation off course. Mary's definition of true teacher has no bearing on how a teacher earns a livelihood but rather on how deeply (or "truly") that teacher is committed to the art/craft/profession of teaching. Just as a true artist might be said to be an artist who creates art regardless of its monetary value, so a true practitioner of any a/c/p might be one who feels compelled to practice that a/c/p whether anyone will pay or not, and will offer it, at least occasionally, gratis.
Mark's remark may thus be less a superfluity than an oblique objection to John's seemingly uncomprehending and rebuking reply to Mary. Yes, of course, a true teacher, on Mary's definition, may make a living by teaching, but only if that teacher also sometimes teaches "off the clock" because of a deep love of teaching and learning. Ironically, Mary's definition is clearly meant as a compliment to John, who--like many recipients of compliments--promptly rejects it, by challenging the validity of its premise.
On this analysis, the answer to the OP's question might be that Mark's comment, far from being irrelevant (or obtuse, erroneous, picayune, worthless, petty, impertinent, tangential, flippant, inane, or senseless), is actually an attempt to steer the conversation back into the course set by Mary.