Definition of "Jewish origin" by the Association of Hebrew Catholics

What is the definition of "Jewish origin" according to the [Association of Hebrew Catholics](https://www.hebrewcatholic.net/) ? - Would children of a Jewish father and a non-Jewish mother be considered to have "Jewish origin" by the Association of Hebrew Catholics? What about children of a Jewish mother? - When a Catholic has only one Jewish ancestor (say in cases where it is matrilineal or patrilineal) and *was a convert to Judaism*, conversions to which movement of Rabbinic Judaism (Orthodox, Conservative or Reform) or non-Rabbinic (Messianic, Haymanot or Karaite) would constitute "Jewish origin" in the case of this Catholic?