We studied the link between the water-mediated (tensile or compressive) strain-driven hydration free energy changes in the association process involving finite-size graphene surfaces, the resulting water-graphene interfacial behaviour, and the combined effect of surface strain and fluid confinement on the thermodynamic response functions and the dynamics of water. We found that either small surface corrugation (compressive strain) or surface stretching (tensile strain) is able to enhance significantly the water-graphene hydrophobicity relative to that of the unstrained surface, an effect that exacerbates the confinement impact on the isothermal compressibility and isobaric thermal expansivity of confined water, as well as on the slowdown of its dynamics that gives rise to anomalous diffusivity.