Using a minimal model approach for interpreting the intermediate scattering function, F(Q, t), to analyze quasi-elastic neutron scattering (QENS) data from interlayer water as a function of temperature in the 2D-layered clay minerals montmorillonite (Mt) and hectorite (Ht) a clear difference in behavior was observed. This was related to the polarization effect induced on the water molecules by both the exchangeable cation and surface charge within the interlayer. Although crucial for improving the wide range of industrial applications of clays as well as for explaining water uptake and retention by clays such information is neither obtained straightforwardly by other experimental methods nor fully accounted by molecular dynamics simulations. Furthermore, analysis of the evolution of the fitted parameters as a function of temperature shows that hydrogen atoms have a relaxation with a smaller average motional amplitude for Mt. Physically this can be explained as stronger hydrogen-bonding by water at the interlayer surfaces in Mt. These results allow for a novel and realistic description of these nanomaterials at the atomic scale, which is crucial for improving functional properties. These findings also prove that this new approach to modeling QENS captures subtle changes hidden in the spectra.