  We apply common gravitational wave inference procedures on binary black hole
merger waveforms beyond general relativity. We consider dynamical Chern-Simons
gravity, a modified theory of gravity with origins in string theory and loop
quantum gravity. This theory introduces an additional parameter $\ell$,
corresponding to the length-scale below which beyond-general-relativity effects
become important. We simulate data based on numerical relativity waveforms
produced under an approximation to this theory, which differ from those of
general relativity in the strongly nonlinear merger regime. We consider a
system with parameters similar to GW150914 with different values of $\ell$ and
signal-to-noise ratios. We perform two analyses of the simulated data. The
first is a template-based analysis that uses waveforms derived under general
relativity and allows us to identify degeneracies between the two waveform
morphologies. The second is a morphology-independent analysis based on
BayesWave that does not assume that the signal is consistent with general
relativity. The BayesWave analysis faithfully reconstructs the simulated
signals. However, waveform models derived under general relativity are unable
to fully mimic the simulated modified-gravity signals and such a deviation
would be identifiable with existing inference tools. Depending on the magnitude
of the deviation, we find that the templated analysis can under perform the
morphology-independent analysis in fully recovering simulated beyond-GR
waveforms even for achievable signal-to-noise ratios $\gtrsim 20{-}30$.
