  Gravitational-wave observations of binary black holes provide a suitable
arena to test the fundamental nature of gravity in the strong-field regime.
Using the data of the inspiral of 29 events detected by the LIGO-Virgo
observatories, we perform a theory-agnostic test of the Kerr hypothesis. We
compute the leading-order deviation to the gravitational waves emitted in the
frequency domain and provide constraints on two deformation parameters
($\delta_1$ and $\delta_2$) belonging to a general class of axisymmetric
non-Kerr black hole spacetimes proposed by Konoplya, Rezzolla & Zhidenko. Our
study shows that all the analyzed events are consistent with the Kerr
hypothesis. The LIGO-Virgo data provide stronger constraints on $\delta_1$ and
$\delta_2$ than those obtained in our previous studies with X-ray data (Papers
I and II), while, on the other hand, they cannot constrain the other
deformation parameters of the Konoplya-Rezzolla-Zhidenko metric ($\delta_3$,
$\delta_4$, $\delta_5$, and $\delta_6$).
