(Today’s Halacha was delivered by the great Gaon Rabbi Gidon Ben Moshe, a prominent Rosh Kollel from Jerusalem)
When Tisha B’Ab falls on Shabbat, as it does this year, the observance is delayed until Sunday. In such a case, Habdala is not recited on Mosa’eh Shabbat, as wine may not be drunk, and it is recited instead on Sunday night, after the fast. We do, however, add "Ata Honantanu" to the Amida of Arbit on Mosa’eh Shabbat, just as on an ordinary Mosa’eh Shabbat.
An interesting question arises in a case where one forgot to add "Ata Honantanu" in the Amida in this situation. Generally, on an ordinary Mosa’eh Shabbat, one who forgot to recite "Ata Honantanu" does not repeat the Amida, since he will in any event be reciting Habdala over a cup of wine. However, if one did not recite "Ata Honantanu," and he also made the mistake of eating before reciting Habdala, then he must repeat the Amida. In this case, he made two mistakes – he omitted "Ata Honantanu," and he ate before Habdala – and the Sages therefore imposed a penalty and required that he repeat the Amida.
A similar situation could arise when Tisha B’Ab falls on Mosa’eh Shabbat. Of course, it is unlikely that somebody would mistakenly eat, as it is a fast day, but it could happen that somebody would mistakenly perform Melacha (activity forbidden on Shabbat) before reciting "Baruch Ha’madbil Ben Kodesh Le’hol." In this case, too, the person has committed two mistakes – he neglected to add "Ata Honantanu" in the Amida, and he performed Melacha before reciting "Baruch Ha’mabdil Ben Kodesh Le’hol." The Rashba (Rabbi Shelomo Ben Aderet of Barcelona, 1235-1310) indeed writes that a person in this case must repeat the Amida. Since he committed two wrongs by forgetting "Ata Honantanu" and performing Melacha before reciting "Baruch Ha’mabdil," he is penalized and must repeat the Amida. However, the Be’ur Halacha (Rabbi Yisrael Meir Kagan of Radin, 1839-1933) notes that the Rambam appears to rule otherwise, and does not require one to repeat the Amida in such a case. In light of the Rambam’s ruling, the Be’ur Halacha writes that one should not repeat the Amida if he forgot "Ata Honantanu" and then ate without reciting "Baruch Ha’mabdil."
Clearly, however, it is best to avoid this situation. And therefore, if one forgot to add "Ata Honantanu" to the Amida on Mosa’eh Shabbat which is Tisha B’Ab, he should ensure to recite "Baruch Ha’mabdil Ben Kodesh Le’hol" immediately after the Amida, so that he does not perform any Melacha before making this recitation.
Summary: When Tisha B’Ab begins on Mosa’eh Shabbat, the paragraph of "Ata Honantanu" is added to the Amida of Arbit as usual. If one forgot to recite "Ata Honantanu" in this case, he does not repeat the Amida, and should recite "Baruch Ha’mabdil Ben Kodesh Le’hol" immediately after the Amida.
