Berakhot 29B

הא דאדכר בתר ״שומע תפלה״.

This case, where we require him to return to the beginning of the prayer and repeat it, refers to a situation where he recalls his error after he reaches the blessing: Who listens to prayer, in which case the option of asking for rain in that blessing no longer exists and he must return to the beginning of the prayer.

אמר רבי תנחום אמר רב אסי אמר רבי יהושע בן לוי: טעה ולא הזכיר של ראש חדש ב״עבודה״⁠ — חוזר ל״עבודה״. נזכר ב״הודאה״⁠ — חוזר ל״עבודה״. ב״שים שלום״⁠ — חוזר ל״עבודה״. ואם סיים ⁠— חוזר לראש.

On a similar note, the Talmud cites an additional statement of R' Tanḥum. R' Tanḥum said that Rav Asi said that R' Yehoshua ben Levi said: One who erred and did not mention Rosh Chodesh, the addition: May there rise and come [ya’aleh veyavo] in the blessing of Temple service, the 17th blessing in the Amida prayer, he returns to the blessing of Temple service. So too, if he remembers during the blessing of thanksgiving, he returns to the blessing of Temple service. If he remembers in the blessing: Grant peace, he returns to the blessing of Temple service. If he remembers after he completed the Amida prayer, he returns to the beginning of the prayer.

אמר רב פפא בריה דרב אחא בר אדא: הא דאמרן סיים ⁠— חוזר לראש, לא אמרן אלא שעקר רגליו, אבל לא עקר רגליו ⁠— חוזר לעבודה.

Rav Pappa son of Rav Aḥa bar Adda said: That which we said that if he already finished the Amida prayer he returns to the beginning, we only said that in a case where he already moved his feet from where he stood in prayer. However, if he did not yet move his feet, he need only return to the blessing of Temple service, and include the addition for Rosh Chodesh therein.