that happens to scale with air density. When the flow is straight and columnated a mass flow is easily calculated. However if the flow has a swirl to it, the rotational component adds to the airspeed. This causes the sensor to over-report mass flow. My guess is that when air is forced in from one side, the imbalance creates a vortex/swirling that has that effect.
The screens are there for this very reason... they help to columnate the flow to improve accuracy. I don't expect there to be very much of a pressure drop across the screen... it would likely more than pay for itself with the improved accuracy and repeatability.
