The single particle dynamics of water confined in a hydrophobically modified MCM-41-S sample has been studied using three high resolution quasielastic neutron scattering spectrometers in the temperature range from 300 to 210 K. A careful modeling of the dynamics allowed us to obtain good agreement among the results obtained with the three instruments, which have very different energy resolutions. The picture arising from the data is that, because of the heterogenous environment experienced by the water molecules, the dynamics show a broad distribution of relaxation times. However, the Fickian diffusive behavior is retained. In the investigated temperature range we found no evidence of the dynamic crossover, from a non-Arrhenius to an Arrhenius behavior, which was detected for water confined in hydrophilic MCM-41-S. This finding is in agreement with what was reported by Chu et al. [Phys. Rev. E 76, 021505 (2007)] for water confined in other hydrophobic confining media that the dynamic crossover takes place at a much lower temperature. The results reported in the paper help clarify the role that the chemical interaction between the water molecules and the walls of the confining host plays in determining the characteristics of the water dynamics, as compared to purely geometric constraints such as the size and shape of the pores.