So that's my problem. Whenever I put one as an exhaust fan, they're nearly silent. But as an intake they make a lot of annoying mid pitch sound. Is there something I can do without modifying the honeycomb grill? Would changing the fan to a 120mm Noctua make a difference?
The noise you're hearing is probably air hitting resistance (Like the drive cages).
The front fans always seem to be louder because of those cages. It's unlikely you'll find a better fan.
I suggest ramping it down a little bit. Or use the included low-noise adapter (7v).
Changing the fan probably wouldn't make too much difference. I suppose it all depends on the direction of air, quite a lot of the time I see cases where the 140mm option in the front is all-but useless due to the way the extra 20mm is covered by metal where the screws go. I'm not sure what it's like in the R4, but if that's the case (ahuehuehue) it may be beneficial to change to a 120mm fan.
Regardless of what you do to the dust filter, the R4 is a silence optimised case, to do that, it pretty much covers the entire front part with the only space for air being the vents either-side.
I doubt you'll get much difference removing the filter.
I have the same case and experienced the same problem. I tried 120mm and 140mm Noctua fans (all of my fans are Noctuas), several different thicknesses of washers and gaskets (up to 1" stand-off), with and without shrouds - you can moderate the buzz, but the lengths you have to go to eliminate it defeats the purpose of having a fan there in the first place.
I gave up. I replaced the side vent cover, put 140mm NF-A14s in both front slots, rear and top-rear, and high-flow PCI slot covers in back. With that setup, I'm able to keep two non-reference GTX 770 OC GPUs under 70C during benchmarking (68C on the hotter card) with the GPU fans at 60% and case fans at about 80% which is still quiet - just air whooshing sound. Even with the case fans maxed, its louder but not an unpleasant sound - again, just the air whoosh.