After reading this thread and considering all the stuff that's gotten under the hoods of my previous cars, I though adding an air intake screen might be a good idea and decided to try a D.I.Y approach. I have a 2021 M3 (with heat pump).
I figured aluminum window screen would be a good material to use. It has a fine mesh and the opening to blockage ratio is high. After looking things over, I decided that putting it on the cover panel would be easier than fitting and anchoring a piece to the intake port.
I cut the screen to the proper shape with edges that would fold down over the sides of the underside of the vent. I put a strip of 3M 9475LE double sided tape on the sides of the vent and bent the edges of the screen onto them. I then put aluminum foil tape over the sides. I put a double layer of foam "truck cap" tape where there was a gap in the intake port foam. I hope it all holds up over time.
Also, while I had the cover panel off, I put dots cut from blue electrical tape on the outside of the panel marking the positions of the clips, to make it easier to know where to pull or push to remove or reinstall it.
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