greetings

Usayd ibn Hadayr (r.a.a.) says:

I said:

O Messenger of Allah

جَزَاكَ اللّٰهُ خَيْرًا

The Prophet (ﷺ) said:

وَأَنْتُمْ فَجَزَاكُمُ اللَّهُ خَيْرًا

(And you too, May Allah reward to with Khayr).

[3096, al-Ta'leeqaatul hisaan.
6231, ibn Hibbaan]

... Shaykh al-Albaany (r.h.) has said that the Hadeeh is Saheeh.

Reply of jazak allahu khiran.

Shouldn't give thanks to another Muslim.

تَقَبَّلَ اللّٰهُ مِنِّيْ وَمِنْكَ

[May Allah accepts you & me (deeds)]

This is how the companions (sababiyyat ridwanullahi 'alaihi) used to greet each other on the day of Eid.

We shouldn't say, "Eid Mubarak".