  The discovery of gravitational waves (GWs) from the compact binary components
by LIGO/Virgo Collaboration provides an unprecedented opportunity for testing
gravity in the strong and highly dynamical field regime of gravity. Currently a
lot of model-independent tests have been performed by LIGO/Virgo Collaboration
and no any significant derivation from general relativity has been found. In
this paper, we study the parity violating effects on the propagation of GWs in
the Nieh-Yan modified teleparallel gravity, a theory which modifies general
relativity by a parity violating Nieh-Yan term. We calculate the corresponding
parity violating waveform of GWs produced by the coalescence of compact
binaries. By comparing the two circular polarization modes, we find the effects
of the velocity birefringence of GWs in their propagation caused by the parity
violation due to the Nieh-Yan term, which are explicitly presented in the GW
waveforms by the phase modification. With such phase modifications to the
waveform, we perform the full Bayesian inference with the help of the open
source software {\texttt Bilby} on the GW events of binary black hole merges
(BBH) in the LIGO-Virgo catalogs GWTC-1 and GWTC-2. We do not find any
significant evidence of parity violation due to the parity violating Nieh-Yan
term and thus place an upper bound on the energy scale $M_{\rm PV} < 6.5 \times
10^{-42} \; {\rm GeV}$ at 90\% confidence level, which represents the first
constraint on the Nieh-Yan modified teleparallel gravity so far.

General Relativity and Quantum Cosmology;High Energy Astrophysical Phenomena;High Energy Physics - Theory