  Power spectrum estimators are an important tool in efforts to detect the 21
cm brightness temperature fluctuations from neutral hydrogen at early times. An
initial detection will likely be statistical in nature, meaning that it will
not be possible to make a coherent map of the brightness temperature
fluctuations; instead, only their variance will be measured against a
background of noise and residual systematic effects. Optimal Quadratic
Estimator (OQE)-based methods often apply an inverse covariance weighting to
the data. However, inaccurate covariance modelling can lead to reduced
sensitivity and, in some cases, severe signal loss. We recently proposed a
Bayesian method to jointly estimate the 21 cm fluctuations, their power
spectrum, and foreground emission. Instead of requiring a fixed a priori
estimate of the covariance, we estimate the covariance as part of the
inference. Choices of parametrization, particularly of the foregrounds, are
subject to model errors and could lead to biases and other ill effects if not
properly controlled. In this paper, we investigate the effects of inaccurate
foreground models on 21 cm power spectrum recovery. Using simulated
visibilities, we find that, even in the most extreme scenarios tested, our
approach is capable of recovering 21 cm delay power spectrum estimates
consistent with a known input signal for delays $\gtrsim300$ ns ($\sim$88\% of
the available Fourier modes). This is true even when using foreground models
derived from modified foreground catalogs containing spatial and spectral
perturbations at the quoted level of uncertainty on our foreground catalogs.
