I’ve heard it said that the woman referred to in Genesis 3:15 is Eve, not Mary. What does the Church teach?
Pope Pius IX, in his dogmatic bull Ineffabilis Deus, says the following:
These ecclesiastical writers in quoting the words by which at the beginning of the world God announced his merciful remedies prepared for the regeneration of mankind . . . saying, "I will put enmities between you and the woman, between your seed and her seed" taught . . . that his most Blessed Mother, the Virgin Mary, was prophetically indicated; and, at the same time, the very enmity of both [Mary and her Son] against the evil one was significantly expressed.
And Pope John Paul II taught in Mulieris Dignitatem:
It is significant that [in Galatians 4:4] St. Paul does not call the Mother of Christ by her own name, "Mary," but calls her "woman": This coincides with the words of the Protoevangelium in the book of Genesis (cf. Gen. 3:15). She is that "woman" who is present in the central salvific event that marks the "fullness of time": This event is realized in her and through her.