I hear the feedback plainly when I listen to it with near field speakers, and it's very obvious in headphones.
Sounds like electrical feedback to me, not something physical. To reduce this stuff, you increase gain on the microphone so that it records it at a higher level and the peaks of the sound you want to keep will be higher dB, then in post, you lower the sound level and the noise floor drops to nothing, but you end up keeping the amplified peaks. This is why the microphones have a +10db or similar switch on them, for this very purpose, to remove backround/noisefloors, but you do it in post. By the way, every +5db doubles audible apparent volume, so +10 and +15 db on these microphones is 2 and 4 times louder. This is why you record it so loud, so you can then, in post, lower the sound level and the noise floor goes with it.