If the noise is fairly constant and homogeneous, Audacity can probably help you remove it. it is an open source program with great features that a lot of instructors use to edit their audio files.
But since it only works with audio, you would have to separate the audio from your video and export it to an audio-only file.
If you asked me a year ago, I would've told you to get an expensive mic. However, more recently, I've been creating screencast videos with apple earphones plugged into my laptop and the sound is just as good. Note: I create all my videos in my bedroom which isn't very large and has carpet.
Many would argue that you should use Audacity, and I've done that in the past. This takes a lot of time, so here's what I converted to:
First, I should let you know that I have a Blue Yeti microphone (great mellow tones but notorious for picking up unwanted sounds) and place it in front of a Dell XPS 27 All-in-one computer that positioned a computer fan about a foot behind my very sensitive mic.
After trying to build various sound buffers, I ultimately bought a Kaotica Eyeball to put over the top of the microphone. This thing is expensive ($199) but advertised as a sound studio in a ball. Here is my setup:
P.S. I am not a Kaotica affiliate or representative ;-).
Then, within Camtasia 2019, I add just a touch of noise reduction to get rid of the residual machine noise. The hardest part in judging the result is hating your own voice ;-), but I receive good feedback on my voice recordings.
Hope this helps,
better to use equipment that introduces no noise, than having it introducing noise and then trying to kill it, because the latter is a very difficult task. The reason why most people get noise is because they use a built in microphone, which all have a poor noise to signal ration, and a very bad sound too. A good microphone has the signal much higher than the noise, which means the latter won't be heard anymore.