Hi Bob,
Hmmm. . .I've never really noticed thumb noice. . .
You may be pressing too hard with your thumb? It shouldn't be used to hold up the neck at all. Also, the proper way to hold your thumb is with the tip pointing out away from the neck slightly so that the skin just above the first joint is touching the neck, not the thumb tip. . .
If you use the thumb tip then there's a greater tendency to use too much pressure and so maybe that is your situation? If not, do you have nylon string instead of the traditional fret thread?
I'll have pics of this on my site within a few weeks. . . . .that's my 2 cents worth. . .
A very good fret cord to try is a product called "STRINGTH". Do a search on google and you'll find it. The #5 is the proper thickness. The gold color goes well with Mangla teaks.
I did noticed some thumb noises too, :-\ but the worse is produced by the finger tips on each side of the callus while gliding over the frets. :-)
I came up with a variation of Nikhil Banerjee's run technic (the use the first finger and the thumb like the clamp of a lobster). So, between 2 "clamps", I release the entire hand from the neck; the thumb barely touching the back and the other fingers totaly off the frets while keeping the string inside the callus grooves. :-)
Now I don't know if this is a good approch for fast runs. Only a master or an advanced sitarist could tell.
I have noticed amother annoyng noise. . :-\ When the finger pushes the string to a fret, it produces 2 notes: the note we try to acchieve and this high pitch & out of tune note produced by the other portion of the string, the one from the "clamped" fret to some previous fret or the top of the neck. .
If those high notes would be in tune with the music, it would be cool and even subtil, but it's not the case. . Any comments?