Although the Shulhan Aruch does not specifically mention whether or not women are obligated in Birkat Hagomel, and Rabbi Haim Benveniste (Knesset Hagedola, § 219) says that there is no difference between women and men and they are equally obligated. The Magen Avraham (219:1) on the other hand, says that Birkat Hagomel has the status of “Reshut”, or a voluntary prayer, and thus women are not obligated in reciting it. Rabbi Eliyahu Spira (Elya Rabba 219:12) is clear in his position that women do not recite it. Furthermore, some Poskim maintain that since one of the requirements is for Birkat Hagomel to be recited in front of a Minyan and women do not participate in a Minyan, they are not obligated in this blessing. The Mishna Berurah (O.H. 219:3) writes that indeed the custom is that women do not recite Hagomel, (c.f. Minhat Shlomo, vol. II, § 4:31) .
Rabbi Shalom Messas (Shemesh Umagen, vol. III, Orah Haim, § 60), and Rabbi Shlomo Dayan (Ateret Shlomo, § 11) all write that the custom in Morocco is for women not to recite Birkat Hagomel, even after giving birth.
Rabbi Ovadia Yosef ( see Yalkut Yosef, Orah Haim § 219), on the other hand, says that women who give birth or overcame a serious illness should reciteBirkat Hagomel. In any case, it appears that even those who follow this opinion hold that women would not recite this blessing after travelling and indeed, this seems to be a popular practice. Since Birkat Hagomel is likened to a Korban and women would bring a Korban after giving birth, one may suggest that nowadays, in place of a Korban, they took upon themselves to recite Hagomelparticularly after childbirth. However, as mentioned, the authentic custom was that women would never recite Hagomel.
Summary: The Moroccan custom is that women do not recite BirkatHagomel, even after giving birth. If a woman wishes to recite it after giving birth, she may do so, but no for the other situations which normally warrant this blessing.