Can't tell what's above the room, but if possible, a ceiling vent would be a good idea. As far away from the fan as possible - and it wouldn't look out of place, would save the door, and be simple to change with a piece of plasterboard later if needed.
Make sure the filters were installed in the unit. They are sometimes left out during construction when the units are tested due to all the dust. they might have forgot to install them. If they are there, clean them or replace them. Not really a good idea to disable ventilation units.
If your ventilator is exhausting air from the apartment, then air (and dust) are being drawn in someplace. If the ventilator filters air and discharges it back into the apartment , it is not a problem.