What should be done regarding the preacher who ordered someone who entered the mosque and prayed two rak'ahs for greeting the mosque to sit down?

If a Muslim enters the mosque while the Imam is delivering the sermon, it is Sunnah for him to pray two rak'ahs before sitting down, according to the Hanbalis and Shafi'is. In contrast, the Malikis forbid it, and it is considered disliked by the Hanafis.

What the Khatib (preacher) did by preventing the "Tahiyyat al-Masjid" (greeting of the mosque) prayer is not considered blameworthy. He might be following some scholars who believe it is not permissible at this time, especially if he is in a country where the Maliki madhhab (school of thought) is prevalent.

The Khatib can be gently reminded after the prayer that the issue is one of scholarly disagreement, and that some scholars permit the "Tahiyyat al-Masjid" during the khutbah (sermon) and have strong evidence for it. It can also be mentioned that a Muslim is not obligated to adhere to a specific madhhab but rather follows the evidence.