Should we pray تحية المسجد (two rak'ahs upon entering the mosque) after performing the congregational prayer that we caught upon entering the mosque?

What the questioner did, entering with the Imam and abandoning the two rak'ahs for greeting the mosque, is correct, due to the saying of the Prophet, peace and blessings be upon him: "If the prayer is established, then there is no prayer except the obligatory one." The obligatory prayer suffices for greeting the mosque.