No circuits exist in hearing aids that can totally remove noise and leave speech. Directional microphones can accomplish that task to some degree, but if the hearing aid does not have directional microphones or if the situation is such that the directional microphones will not help, the hearing aid itself cannot clean up a niosy signal.
These circuits work by removing the pitch ranges that seem to be dominated by noise.The problem is that speech covers the entire bandwidth of the hearing aid. If any pitch ranges are removed in order to remove noise, speech information will also be removed. This approach works particularly well for constant noises, such as a refrigerator running or the hum of a computer.
Now, if this removal is done with a more gentle hand (meaning that the amount of reduction is limited), then the loudness or annoyance of the noise level can be reduced. You may not understand speech any better (since no new information is added to the signal), but you may find the response of the hearing aid to be more acceptable.
A newer apporach is to reduce the amplification during times when no speech is present. This approach allows the ear to have a break when no one is talking but then restores the full signal when the speech starts again. The goal is that throughout the course of the day, the ''fatigue'' factor of using a hearing aid is reduced.