All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The abrogated verse about breastfeeding to which ʻAa’ishah referred was cited in some authentic hadiths. Muslim narrated that ʻAa’ishah, may Allah be pleased with her, said, "It was revealed in the Quran that ten definite breastfeedings establish the Mahram (permanently unmarriageable) relationship, then it was also revealed that five definite breastfeedings establish it." [Muslim]
In a version of this hadith cited by Ibn Maajah and classified as authentic by Al-Albaani: "Among what was revealed of the Quran and was then abrogated is that nothing establishes the Mahram relationship except ten breastfeedings or five definite ones." [Ibn Maajah]
As for the statement that the verse to which ʻAa’ishah referred does not exist, then the answer is that this verse is not in the Mus-haf (physical copy of the Quran) because it was abrogated as a recited verse and as a ruling. Al-ʻIraaqi said, "An example of the verses whose ruling and recitation were both abrogated is the one referred to in the hadith in Saheeh Muslim on the authority of ʻAa’ishah, may Allah be pleased with her: 'Among what was revealed is that ten definite breastfeedings establish the Mahram relationship, then they were abrogated by five.'" [Al-Ghayth Al-Haamiʻ Sharh Jamʻ Al-Jawaamiʻ]
As for the hadith cited in Al-Muwatta’, its chain of narration is authentic, as stated by Shaykh ʻAbd Al-Qaadir Al-Arnaa‘oot in his book Tahqeeq Jaamiʻ Al-Usool of Ibn Al-Atheer.
For more benefit, please refer to fatwas 182309 and 86750.
Allah knows best.