Is تحية المسجد (the prayer for greeting the mosque) performed upon entering the mosque for the Eid prayer?

The Sunnah is to perform the Eid prayer in the Musalla (outdoor prayer area). It should not be performed in the mosque unless there is a need, such as rain or intense heat. If it is prayed in the mosque, then the person entering should pray two rak'ahs as a greeting to the mosque (Tahiyat al-Masjid) before sitting down and before the Imam arrives. However, if it is prayed in the Musalla, then Tahiyat al-Masjid is not legislated, because it does not have the ruling of a mosque in that regard.