How to filter out Morse-like noises

I am trying to clean a recording that has a Morse-like noise in the background (

). It is basically a noise that comes and goes, with energy around 2-3 KHz.
I have tried using noise removal in Audacity but it does not work well in eliminating this random on/off effect. I am hesitant to apply a band-pass filter to the whole signal because I have speech parts that would get heavily degraded by it.
Is there anything I can do to improve the quality of my audio (i.e. reduce the amount of Morse noise)


Unfortunately, it is intermittent broadband noise (broad frequency range and intermittent), which is virtually impossible to remove without causing significant damage to the remaining audio.

Thanks for your answer.
Even if the signal gets a bit deteriorated, what would be the best procedure to eliminate this noise?
For example, is it possible in Audacity to train a band-pass filter given some data?

Although the “morse-like” noise is mostly 1- 3 kHz, there are overtones up to about 15kHz that become evident after removing the most “visible” part. It is also difficult to remove the loudest part of the noise because it tends to leave an audible “hole” in the sound. With careful application of a mid-shelf filter, the main part of the noise may be reduced to roughly match the surrounding noise, but the process is very fiddly and must be repeated with new settings for every “tap”. The overtones then need to be removed with localised filtering. I would estimate that, with practice, you could fix 1 minute of recording with about 40 hours of editing. Is it worth it?