If the woman had a valid conversion, followed by a valid halachic marriage to a Jew, and subsequently bore a child to a non-Jewish male without have received a “get”, that child would arugably be a “mamzer”. In practice, if the putative mamzer (or his/her descendant)then became a Baal Tseuvah, a Beis Din would look at the validity of the mother’s initial marriage, and the validity of the conversion – since Beitei Din “bend over backwards” to avoid deciding that someone is a mamzer.
Those who said that the status of the non-Jewish father is irrelevant were addressing a situation where the mother is an unmarried Jews whereas in the “question” here she is said to be a woman married according to halacha.