Finding Transfer Response
The whole point of the frequency discriminator is to have some output voltage which depends on the frequency shift \$\Delta f\$. In time domain you have this signal at the output of the discriminator:

\[
V(t) = \Delta V(\Delta f) \cdot 
 \sin\left[2 \pi\; f_m \left(t - \frac{\tau_d}{2} \right) \right]
\]

I.e. you have a sinusoidal signal whose amplitude holds the information about the frequency variations of the input. Therefore, in a system perspective, the relationship between your "input" \$\Delta f\$ and the desired output \$\Delta V\$ is independent of the sinusoidal signal time variations. 

In other words, by "transfer response" it is meant the relationship between the amplitude of \$V(t)\$ versus \$\Delta f\$.