We apply third-moment theory that describes the energy cascade within the inertial range of magnetohydrodynamic turbulence to observations of large cross-helicity states at 1 AU. We find that in contrast to intervals with smaller helicity that form the bulk of the observations, large helicity states demonstrate a significant back-transfer of energy from small to large scales. This occurs in such a manner as to reinforce the dominance of the outward-propagating fluctuations. We find no evidence of a significant anisotropy in the back-transfer dynamics and conclude that the process must be short-lived in order to be consistent with solar wind observations. We offer this as partial explanation for large helicity states in the solar wind.