Just like for tuning a guimbarde, the maker is adding some wax on the moving part, making it a bit heavier, just like a spring mass system it will make the resonance frequency lower. This allows to tune the guimbarde to a chosen note.
I would guess the Syahi's goal is exactly: tuning. The more you have on the lower the note you get. Thus removing it you will get an higher pitch, and adding more you'll get a lower pitch, as the skin will be "heavier".
For worn skin, it is probable that they will more or less flexible than what it was originally. Just like for the spring, it will change the frequency of the note you get (say the resonant mode or fundamental), thus getting the Tabla out of tune. Adding or removing some Syahi will get back in tune by adjusting the mass of the skin, which is also influencing the resonant frequency of your system.
(Small) Math/Physics addon
Just for precision: a spring mass system resonant frequency is given by:
f = 1/(2pi)*sqrt(k/m)
with k the spring constant and m the mass. Thus, if you have a change in the skin (acting kind of like a spring) you can compensate it with mass to get the same frequency. Obviously, a skin is not exactly a pure mass-spring system, so the above equation is probably incorrect in the quantitative way… However, the physics is the same and thus the dependencies over the spring constant and mass are likely to be going the same way:
- adding mass reduce the resonance frequency
- an "harder" skin will increase the resonance frequency