This is a study to identify predicted effects of the carbon nucleus environment on neutrino - nucleus interactions with low momentum transfer. A large sample of neutrino interaction data collected by the MINERvA experiment is analyzed to show the distribution of charged hadron energy in a region with low momentum transfer. These distributions reveal a major discrepancy between the data and a popular interaction model with only the simplest Fermi gas nuclear effects. Detailed analysis of systematic uncertainties due to energy scale and resolution can account for only a little of the discrepancy. Two additional nuclear model effects, a suppression/screening effect (RPA), and the addition of a meson exchange current process (MEC), are shown to improve the description of the data.