Berakhot 49B

והדר לרישא. אמר ליה: מאי טעמא עביד מר הכי? אמר ליה, דאמר רבי שילא אמר רב: טעה ⁠— חוזר לראש.

and he returned to the beginning of Grace after Meals and repeated it. Giddel bar Manyumi said to Rav Naḥman: Why did the master act in that manner? He said: As R' Sheila said that Rav said: If one erred, he returns to the beginning.

והא אמר רב הונא אמר רב: טעה ⁠— אומר ״ברוך שנתן״! אמר ליה: לאו איתמר עלה, אמר רב מנשיא בר תחליפא אמר רב: לא שנו אלא שלא פתח ב״הטוב והמטיב״, אבל פתח ב״הטוב והמטיב״⁠ — חוזר לראש.

Giddel bar Manyumi challenged: Didn’t Rav Huna say that Rav said: If one erred, he recites: Blessed…Who gave? Rav Naḥman said to him: Wasn’t it stated about this that R' Menashya bar Taḥlifa said that Rav said: They only taught that one recites the short blessing in a case where he did not yet begin reciting: Who is good and does good; however, if he already began reciting: Who is good and does good, he must return to the beginning of Grace after Meals?

אמר רב אידי בר אבין אמר רב עמרם אמר רב נחמן אמר שמואל: טעה ולא הזכיר של ראש חדש בתפלה ⁠— מחזירין אותו. בברכת המזון ⁠— אין מחזירין אותו.

Rav Idi bar Avin said that Rav Amram said that Rav Naḥman said that Shmuel said: If one erred and did not mention the formula for Rosh Chodesh in his Amida prayer, we require him to return to the beginning of the prayer and repeat it. However, if one erred and forgot to mention Rosh Chodesh in Grace after Meals, we do not require him to return to the beginning and repeat it.

אמר ליה רב אבין לרב עמרם: מאי שנא תפלה ומאי שנא ברכת המזון? אמר ליה: אף לדידי קשיא לי ושאילתיה לרב נחמן, ואמר לי: מיניה דמר שמואל לא שמיע לי, אלא נחזי אנן: תפלה דחובה היא ⁠— מחזירין אותו. ברכת מזונא, דאי בעי אכיל אי בעי לא אכיל ⁠— אין מחזירין אותו.

Rav Avin said to Rav Amram about this: What is the difference between the Amida prayer and Grace after Meals? He said to him: That question was also difficult for me and I asked Rav Naḥman about it, and he said to me: I did not hear the reason from Mar Shmuel himself, but let us see if we can analyze it ourselves. For the Amida prayer, which is an obligation, we require him to return to the beginning of the prayer and repeat it. For Grace after Meals, which is not an obligation, as if he wants to eat, he eats and if he wants not to eat, he does not eat, we do not require him to return to the beginning and repeat it. Grace after Meals is not a full-fledged obligation; it is dependent upon eating, which is optional. Consequently, failure to mention Rosh Chodesh in Grace after Meals is not a source of concern.