  Interferometric experiments designed to detect the highly redshifted 21-cm
signal from neutral hydrogen are producing increasingly stringent constraints
on the 21-cm power spectrum, but some k-modes remain systematics-dominated.
Mutual coupling is a major systematic that must be overcome in order to detect
the 21-cm signal, and simulations that reproduce effects seen in the data can
guide strategies for mitigating mutual coupling. In this paper, we analyse 12
nights of data from the Hydrogen Epoch of Reionization Array and compare the
data against simulations that include a computationally efficient and
physically motivated semi-analytic treatment of mutual coupling. We find that
simulated coupling features qualitatively agree with coupling features in the
data; however, coupling features in the data are brighter than the simulated
features, indicating the presence of additional coupling mechanisms not
captured by our model. We explore the use of fringe-rate filters as mutual
coupling mitigation tools and use our simulations to investigate the effects of
mutual coupling on a simulated cosmological 21-cm power spectrum in a "worst
case" scenario where the foregrounds are particularly bright. We find that
mutual coupling contaminates a large portion of the "EoR Window", and the
contamination is several orders-of-magnitude larger than our simulated cosmic
signal across a wide range of cosmological Fourier modes. While our fiducial
fringe-rate filtering strategy reduces mutual coupling by roughly a factor of
100 in power, a non-negligible amount of coupling cannot be excised with
fringe-rate filters, so more sophisticated mitigation strategies are required.
