  We present a study of internal reflection and cross coupling systematics in
Phase I of the Hydrogen Epoch of Reionization Array (HERA). In a companion
paper, we outlined the mathematical formalism for such systematics and
presented algorithms for modeling and removing them from the data. In this
work, we apply these techniques to data from HERA's first observing season as a
method demonstration. The data show evidence for systematics that, without
removal, would hinder a detection of the 21 cm power spectrum for the targeted
EoR line-of-sight modes in the range 0.2 < k_parallel < 0.5\ h^-1 Mpc. After
systematic removal, we find we can recover these modes in the power spectrum
down to the integrated noise-floor of a nightly observation, achieving a
dynamic range in the EoR window of 10^-6 in power (mK^2 units) with respect to
the bright galactic foreground signal. In the absence of other systematics and
assuming the systematic suppression demonstrated here continues to lower noise
levels, our results suggest that fully-integrated HERA Phase I may have the
capacity to set competitive upper limits on the 21 cm power spectrum. For
future observing seasons, HERA will have upgraded analog and digital hardware
to better control these systematics in the field.
