Did I Say 'Retzeh V'hachalitzenu'?

Since the commandment of Birkat Hamazon (Grace After Meals) is a Torah obligation, as it is written: "And you shall eat and be satisfied and bless Hashem," therefore one who is uncertain whether they recited Birkat Hamazon or not must repeat it due to uncertainty, following the principle: "When in doubt about a Torah law, be stringent." According to this, it would seem that the same would apply to someone who is uncertain whether they mentioned "Retzeh V'hachalitzenu" on Shabbat, since if one forgot to mention it, the ruling is that one must repeat the blessing, so similarly due to uncertainty, one would need to repeat the blessing.

However, even though Birkat Hamazon is from the Torah, the requirement to mention "Retzeh V'hachalitzenu" in Birkat Hamazon is not from the Torah. Many of our early sages wrote this, including the Rashbatz (Rabbi Shimon bar Tzemach) in his rulings on Berachot (49). Therefore, it seems more appropriate that when one is uncertain whether they mentioned "Retzeh V'hachalitzenu" or not, the ruling is that they do not need to recite the blessing again, following the principle "When in doubt about a rabbinical law, be lenient." This is because according to the Torah, one has fulfilled the obligation of Birkat Hamazon even without mentioning "Retzeh V'hachalitzenu."

However, in Responsa B'samim Rosh, section 287 (mostly attributed to Rabbeinu Asher), it states that since there is a presumption that a person continues their blessing as they are accustomed to blessing throughout the week, it is more likely that they did not mention "Retzeh V'hachalitzenu" in Birkat Hamazon, and therefore they should repeat Birkat Hamazon as in the case of someone who definitely did not mention "Retzeh V'hachalitzenu." This is similar to how we rule regarding someone who, after completing their prayer during the rainy season, is uncertain whether they mentioned "Bestow dew and rain for blessing" in the blessing of the years - we presume they forgot that it was the rainy season and continued with their summer routine when rain is not requested, and thus they must repeat the prayer. The same would apply to mentioning "Retzeh V'hachalitzenu."

After extensively discussing this matter in his book Yabia Omer (Vol. 7, p. 68), Rabbi Ovadia Yosef wrote that although we generally tend to say that there is a presumption that every person continues with their routine in prayer and other matters, nevertheless, regarding Birkat Hamazon on Shabbat, there is reasoning that counters this presumption. Since the awe of Shabbat is upon a person on Shabbat, as the entire atmosphere changes on Shabbat, and people are accustomed to being careful about all Shabbat prohibitions at every moment, there is reason to believe that the person remembered it was Shabbat and did not forget to mention "Retzeh V'hachalitzenu." Although the matter remains uncertain, since we have already explained that the requirement to mention "Retzeh V'hachalitzenu" is only rabbinical and not from the Torah, the principle returns that "When in doubt about a rabbinical law, be lenient," and therefore in such a case, one should not repeat Birkat Hamazon.

In summary: Someone who completed Birkat Hamazon (for the first and second meals) on Shabbat and is now uncertain whether they mentioned "Retzeh V'hachalitzenu" in Birkat Hamazon does not need to repeat Birkat Hamazon, since the main requirement to mention "Retzeh V'hachalitzenu" is only rabbinical. There is no need to be concerned that they likely continued with their weekday routine and did not mention "Retzeh V'hachalitzenu," because against this, one can say that since the awe of Shabbat is upon them, they remembered to mention "Retzeh V'hachalitzenu" in their blessing.

And if after completing the blessing of "Boneh Yerushalayim" one is uncertain whether they mentioned "Retzeh V'hachalitzenu," and they have not yet begun the blessing of "HaTov V'haMeitiv" which follows the blessing of Boneh Yerushalayim, then they should correct the matter by reciting "Blessed are You, Hashem our God, King of the universe" etc.