Specifically the first tutorial, 2mins 40seconds in, they talk about filters on how to remove white noise.
Also, I've used another Open Source software editor called Audacity.
You would need to "fix" the audio separately with audacity and then, once "fixed" bring it back into your Camtasia project. Obviously this would not be ideal, since any editing such as clipping would not be done equally to associated video. Therefore this could result in audio not being in sync with video. However, if you are doing alot of audio editing it is worth checking out audacity. Since it is Open Source, it costs you nothing to try it, and it has alot of very powerful audio editing features you simply wont find in Camtasia.
JPK Services LLC (my company) specializes on open source solutions. Please feel free to email us questions or inquiries. We have a vast knowledge base of open source software, what their feature sets are and how to effectively use them.
Hard to know what to recommend because we don't know what or where you're recording and what equipment is being used. Were you recording a browser window or a program screen? Was it system audio recorded? From a headset or other microphone, etc.?
With details we might be able to help further; please provide more to understand.