A vague memory suggests "It was all My eye and Betty Martin" may have been a nautical mondegreen: a sailor venturing ashore in a Catholic country, happening on a Mass being celebrated, and being asked back on the ship what it was like. Determining quite what from the Latin mass was misheard as "my eye and betty martin" is left as an exercise for the student, but I remember thinking "that makes sense" when I saw it.

.... When Herself goes to Mass next, I'll ask her to ask the priest. Research continues.