Abu Hurairah (may Allah be pleased with him) narrated that the Prophet (ﷺ) said:
تكفير كل لحاء ركعتان
The expiation for every argument/dispute is two rak’aat
[Authenticated by Shaikh al-Albani in the Saheeha (no. 1789) and Saheeh Jami (no. 2986)]
Imam as-San’aani (may Allah have mercy upon him) said in explanation of the narration:”That is: a dispute and insult. So it is necessary for the one who argues and insults [another] that he expiates it.
(Two Rak’at): it is as if the two rak’aat expiate the sin of obscenity. As for the right of the one he insults, then it is not dropped except by his pardoning…” [Tanweer Sharh Jami as-Sagheer (5/89)]
Imam al-Munaawi (may Allah have mercy upon him) said: “(Two Ra’kat): which he prays after making wudu for them. Verily it [the wudu] removes anger as it comes in a narration which will come [later]” [Fayd ul-Qadeer (3/266)]
So based on this narration, it is recommended to pray two rak’aat after engaging in an argument or insulting someone as a form of expiation.
And Allah Knows best
Faisal bin Abdul Qaadir bin Hassan