Praise be to Allah.
Offering congratulations for Eid is something that is permissible; that was narrated from some of the Sahaabah (may Allah be pleased with them).
Ibn Qudaamah (may Allah have mercy on him) said: Ibn ‘Aqeel quoted some hadeeths about offering congratulations on Eid, including the report that Muhammad ibn Ziyaad said: I was with Abu Umaamah al-Baahili and some of the other companions of the Prophet (blessings and peace of Allah be upon him); when they went back from Eid (prayer), they would say to one another: May Allah accept from us and from you. Ahmad said: The isnaad of the hadeeth of Abu Umaamah is a jayyid isnaad.
End quote from al-Mughni (2/130)
What appears to be the case from the actions of the Sahaabah and what has been narrated from them is that offering congratulations for Eid should come after the Eid prayer. So if a person limits it to that, that is good, as it is following the example of the Companions of the Prophet (blessings and peace of Allah be upon him). But if he offers such congratulations before that, to be the first to give this greeting to his friend, it seems that there is nothing wrong with that, because offering congratulations for Eid comes under the heading of customs and traditions, and such matters are broad in scope and should be referred to the customs that are prevalent among the people.
Ash-Shirwaani ash-Shaafa‘i (may Allah have mercy on him) said: From his words it may be understood that on the day of Eid, it is not required to congratulate people during the days of Tashreeq or after the day of Eid al-Fitr; rather it has become customary among people to offer congratulations on these days, and there is no reason not to do so, because the aim behind it is to create feelings of friendship and express joy. It may also be understood from his mentioning the day of Eid that the time for offering congratulations begins at Fajr, not the night before, even though there are other views, as mentioned in some commentaries. It may be said that there is nothing wrong with doing it if that is the custom, because of what he mentioned about the aims behind it, namely to create feelings of friendship and express joy. This is supported by the fact that it is recommended to say takbeer on the night before Eid.
End quote from Hawaashi ash-Shirwaani ‘ala Tuhfat al-Muhtaaj (2/57)
And Allah knows best.