Yes, it’s always best to have as little noise as possible in the original audio, but sometimes some noise is unavoidable. And sometimes an audio editor is a better tool for this sort of job than a video editor.
One option to consider, if it’s feasible for you, would be to extract the audio and then use the noise reduction feature of an audio program such as Audacity (another free open source cross-platform program). Audacity’s noise reduction works by you selecting a section that only contains the noise and letting it analyze that noise, so that it knows what your noise sounds like, then applying that noise reduction to the whole clip. To put it simply, things in the clip that sound similar to the noise get reduced, while things that don’t sound like the noise get left alone.
Once you’ve made a less noisy audio file, you could use that instead of the video’s sound. Put the video on one track and in the clip’s properties set the audio to none. Put the cleaned-up audio on an audio track, lined up with the video so that they’re in sync.