  The inspiral-merger-ringdown (IMR) consistency test checks the consistency of
the final mass and final spin of a binary black hole merger remnant,
independently inferred via the inspiral and merger-ringdown parts of the
waveform. As binaries are expected to be nearly circularized when entering the
frequency band of ground-based detectors, tests of general relativity (GR)
currently employ quasicircular waveforms. We quantify the effect of residual
orbital eccentricity on the IMR consistency test. We find that eccentricity
causes a significant systematic bias in the inferred final mass and spin of the
remnant black hole at an orbital eccentricity (defined at $10$ Hz) of $e_0
\gtrsim 0.1$ in the LIGO band (for a total binary mass in the range $65$-$200
\,M_{\odot}$). For binary black holes observed by Cosmic Explorer (CE), the
systematic bias becomes significant for $e_0 \gtrsim 0.015$ (for $200$-$600
\,M_{\odot}$ systems). This eccentricity-induced bias on the final mass and
spin leads to an apparent inconsistency in the IMR consistency test,
manifesting as a false violation of GR. Hence, eccentric corrections to
waveform models are important for constructing a robust test of GR, especially
for third-generation detectors. We also estimate the eccentric corrections to
the relationship between the inspiral parameters and the final mass and final
spin; they are shown to be quite small.
