Yes you are right adsorbtion of sound at 40 khz does increase with humidity.
See the table - Attenuation of sound in air (dB/ km) from:
This will change the amplitude of the received signal.
This is only one of many ways the amplitude of the signal can be changed.
The most significant is turbulence in the air.
My design does not depend on the amplitude of the received signal.
I get the difference in tof along a path and this cancels the amplitude difference.
This does lead to another complication which I have explained in the pdf file.
What could effect the design is change of speed due to humidity variations.
See the table - Speed of sound in air (m /s) in the above site.
The variation is much smaller than for temperature change.
It may add an error of about 1% so I neglect humidity in the design.