Which organelle is responsible for removing foreign material from the trachea and bronchi?

The correct answer is cilia.

Cilia are tiny, hair-like projections that line the respiratory tract, including the trachea and bronchi. They are responsible for removing foreign material, such as dust, pollen, and bacteria, from the airways. Cilia beat in a coordinated fashion, moving foreign material upward toward the throat, where it can be coughed out or swallowed.