There are two Marfu‘ narrations reported regarding this:
1. The Narration Attributed to Sayyiduna Wathilah bin al-Asqa‘ رضی اللہ تعالیٰ عنہ
Al-Kamil by Ibn ‘Adi, Vol. 6, p. 2274; another edition 7/524, where he said: “This is Munkar…” Al-Majruhin by Ibn Hibban 2/301; another edition 2/319; Al-Sunan al-Kubra by al-Bayhaqi 3/319; Al-‘Ilal al-Mutanahiyah by Ibn al-Jawzi 1/476, Hadith 811, where he said: “This is a Hadith that is not authentic…” Al-Tadwin fi Akhbar Qazwin 1/342; Abu Bakr al-Azdi al-Mawsili in his Hadith, Q 3/2, cited in Silsilat al-Ahadith al-Da‘ifah wal-Mawdu‘ah by al-Albani 12/385–386, Hadith 5666.
This narration is Mawdu‘ (fabricated) because of Muhammad bin Ibrahim bin al-‘Ala al-Shami. Regarding the aforementioned Muhammad bin Ibrahim, Imam al-Daraqutni رحمۃ اللہ علیہ said: “A liar.” (Su’alat al-Barqani li al-Daraqutni: 423)
Hafiz Ibn Hibban رحمۃ اللہ علیہ said: “He used to fabricate Hadiths against the Syrians.” (Al-Majruhin 2/301; another edition 2/319)
The author of Al-Mustadrak, Hafiz al-Hakim رحمۃ اللہ علیہ, said: “He narrated fabricated Hadiths from al-Walid bin Muslim and Suwayd bin ‘Abdulaziz.” (Al-Madkhal ila al-Sahih, p. 208, Hadith 191)
2. The Narration Attributed to Sayyiduna ‘Ubadah bin al-Samit رضی اللہ تعالیٰ عنہ
(Al-Sunan al-Kubra by al-Bayhaqi 3/319–320; Amali Ibn Sham‘un: 277; Al-Majruhin by Ibn Hibban 2/149; another edition 2/133; Al-‘Ilal al-Mutanahiyah 2/57–58, Hadith 900, where he said: “This is a Hadith that is not authentic”; Tarikh Dimashq by Ibn ‘Asakir 36/69.)
Regarding its narrator, Abdul-Khaliq bin Zayd bin Waqid, Imam Bukhari رحمۃ اللہ علیہ said:
“Munkar al-Hadith” (Kitab al-Du‘afa lil-Bukhari, tahqiq: 244)
Imam Bukhari رحمۃ اللہ علیہ said: “If I call someone Munkar al-Hadith, then I do not consider it permissible to narrate from him.” (Al-Tarikh al-Awsat 2/107, second edition with Al-Tarikh al-Awsat 3/582)
It is known that this narration is extremely weak. Secondly, it is also disconnected because there is no intermediary between Makhul and Sayyiduna Ubadah رضی اللہ تعالیٰ عنہ. Hafiz Ibn Hajar رحمۃ اللہ علیہ has declared this narration weak in terms of its chain of transmission. (See Fath al-Bari 2/446 under Hadith 952)
After discussing these rejected narrations, the examination of some Athār (reports of the Companions and early scholars) is presented below:
1. Al-Tahawi said:
“قال الطحاوي في مختصر اختلاف العلماء: وحدثنا يحيى بن عثمان قال حدثنا نعيم قال حدثنا محمد بن حرب عن محمد بن زياد الألهاني قال: كنا نأتي أبا أمامة وواثلة بن الأسقع في الفطر والأضحى ونقول لهما : قبل الله منا ومنكم فيقولان: ومنا ومنكم”
“It is narrated from Muhammad ibn Ziyad al-Alhani (Abu Sufyan al-Mahsi, trustworthy) that whenever we would visit Abu Umamah and Wathilah ibn al-Asqa‘ (may Allah be pleased with them) on Eid al-Fitr and Eid al-Adha, they would say:”
“تَقَبَّلَ اللَّهُ مِنَّا وَمِنْكُمْ”
“May Allah accept our deeds and yours.” They would then reply: “And yours as well, and yours as well.”
(Mukhtasar Ikhtilaf al-Fuqaha by al-Tahawi, abridged by al-Jassas, 4/385; its chain of transmission is حسن.)
In this chain of transmission, یحییٰ بن عثمان بن صالح and نعیم بن حماد were regarded as trustworthy (موثق) by the majority of scholars and were therefore considered حسن الحدیث, while the remainder of the chain is صحیح.
Ibn al-Turkumani narrated this report without citing a source and described it as “حدیث جید”. He also narrated from احمد بن حنبل that its chain of transmission is جید. See الجواہر النقی 3/319–320.
2. Qazi Hussain bin Ismail Al-Majahili said:
“عن جبير بن نفير قال : كان أصحاب رسول الله صلى الله عليه وسلم إذا التقوا يوم العيد يقول بعضهم لبعض : تقبل الله منا ومنك”
It is narrated from Jubair ibn Nufair (a Tabi‘i, may Allah have mercy on him) that when the Companions of the Prophet ﷺ met one another on the day of Eid, they would say to each other:
“تَقَبَّلَ اللَّهُ مِنَّا وَمِنْكُمْ”
“May Allah accept from us and from you.”
(Al-Juz’ al-Thani min Kitab Salat al-‘Idayn, an illustrated manuscript, p. 22-B; its chain of transmission is Hasan.)
The chain of this narration is Hasan, and Hafiz Ibn Hajar (may Allah have mercy on him) also classified it as Hasan. See Fath al-Bari, 2/446, under Hadith No. 952.
3. It is narrated from Safwan ibn Amr al-Saksaki (trustworthy) that he saw Abdullah ibn Busr al-Mazini (may Allah be pleased with him), Khalid ibn Ma‘dan (may Allah have mercy on him), Rashid ibn Sa‘d (may Allah have mercy on him), Abd al-Rahman ibn Jubair ibn Nufair (may Allah have mercy on him), Abd al-Rahman ibn ‘A’idh (may Allah have mercy on him), and other scholars greeting one another on Eid by saying:
“تَقَبَّلَ اللَّهُ مِنَّا وَمِنْكُمْ”
“May Allah accept from us and from you.”
(Tarikh Dimashq by Ibn ‘Asakir, 26/106, biography of Safwan ibn Amr; its chain of transmission is Hasan.)
4. Ali ibn Thabit al-Jazari (may Allah have mercy on him), who was Saduq and Hasan al-Hadith, said:
“I asked Imam Malik ibn Anas (may Allah have mercy on him) about people saying “تَقَبَّلَ اللَّهُ مِنَّا وَمِنْكُمْ” to one another on the day of Eid. He replied: ‘This has been the practice among us in Madinah, and we see nothing wrong with it.’”
(Kitab al-Thiqat by Ibn Hibban, Vol. 9, p. 90; its chain of transmission is Hasan.)
5. It is narrated from Imam Shu‘bah ibn al-Hajjaj (may Allah have mercy on him) that he met Yunus ibn ‘Ubaid on the day of Eid, and he said to him:
“تَقَبَّلَ اللَّهُ مِنَّا وَمِنْكُمْ”
(Kitab al-Du‘a by al-Tabarani, Vol. 2, p. 1334, Hadith No. 929; its chain of transmission is Hasan.)
The narrator of this report, Hasan ibn Ali al-‘Umari, was considered Saduq and Hasan al-Hadith in those narrations in which no objection was raised against him. No such objection has been established against him in this narration either. See also Lisan al-Mizan bi-Hawashiyatihi, Vol. 2, pp. 414–415.
6. Al-Tahawi said that when his teachers and contemporaries, Bakkar ibn Qutaybah, Imam al-Muzani, Yunus ibn Abd al-A‘la, and Abu Ja‘far ibn Abi Imran, were congratulated on Eid, they would respond in the same manner.
(Mukhtasar Ikhtilaf al-‘Ulama, Vol. 4, p. 385.)
These reports show that it is permissible to say “تَقَبَّلَ اللَّهُ مِنَّا وَمِنْكُمْ” to one another on the day of Eid and to offer Eid greetings.