First, turn the air vent/cover lock pin counterclockwise from the top of the cover to unscrew it from the cup underneath. Lift the pin out and remove the cup.
Pull the small gasket off the cup's threaded shaft. Wash all parts in warm, soapy water. Use a soft cloth or small nylon brush to clean the cover hole.
To reassemble, put the small gasket back on the cup's shaft. Push the cup's shaft up through the cover hole from underneath. Screw the pin back on clockwise until tight.