The Church can do nothing more than try to remind the Protestant party of their promise. But then again this is one of the reasons many religions discourage intermarriage, it can cause either the loss of faith of one or both parties, or even worse the breakup of a marriage.
Here is a sad example. I know a man who was raised and still believes in the teachings of the Catholic Church. He married an Episcopalian. Early on they raised the first two boys Catholic, then she became pregnant when the youngest son was 16. She wanted to abort because the baby had a higher chance of being born retarded or deformed due to her age. Thank God he was born with no issues, however because she so protested the Catholic teachings about abortion, and felt put upon by the Church and her husband, she insisted the boy be raised in no religion, and now none of them attend any Church, and the boys get no religious formation.
This is an extreme example, but unfortunatly not an uncommon one.