Background noise from your Camtasia Editor recording, such as fans or ambient noise, can be removed by using the Noise Removal tool found in the Audio Effects tab. Simply click and drag the Noise Removal effect onto the audio track containing background noise. Choose Analyze to automate noise removal process. (Windows only). Or, manually adjust the Sensitivity, Reduction (Mac), or Amount (Windows) to get desired effect.
For Noise Removal best practices, see this article: https://support.techsmith.com/hc/en-us/articles/360015185932-Noise-Removal-Best-Practices
Tip: Audiate
Did you know that Audiate has noise removal tools as well? Check it out here: https://www.techsmith.com/learn/tutorials/audiate/remove-noise/