I tried that using Audacity, but get a 'bubbly' sound and a lot of the natural harmonics are lost.
Yes, that is a problem but less of a problem in the other software, GoldWave. I have better control over pecentage cleanup. I can actually see the graphical representation of the song over time and decide what to do. But even there, I use 20-50% correction mostly. I do the corrections incrementally (takes time) and if I sense any loss of music or introduction of tinkilng, I abandon my effort.
It cost about about 50$ a few years back.
The trick is to find a place in the recording where tanpura is not present. Otherwise, it will result in a lot of tinkling noise. For radio recordings, the hum/hiss present when the announcer picks up the mike is an ideal place. Cleans up whole recording nicely.
If you want send me a clip. I will use only Audacity and if successful, I will send you the steps.