Quantum effects in the scattering and desorption process of a water molecule from a graphite surface are investigated using the linearized path integral model. The graphite surface is quantized rigorously using the fully quantum many-body Wigner transform of the surface Boltzmann operator, while the water molecule is treated as rigid. Classical dynamics with these quantized initial conditions show that quantizing the surface at 100 and 300 K results in markedly different results, compared to a fully classical analysis. The trapping probability (defined as the probability of multiple encounters with the surface) is not sensitive to the choice of dynamical treatment, but the residence time on the surface is much shorter in the quantum case. At 300 K the transiently trapped molecules desorb from the surface with a rate constant which is 60-70% larger than the corresponding classical value. Lowering the surface temperature to 100 K decreases the quantum rate constant by approximately a factor of 3 while all trapped molecules stick to the surface in the classical case. The stability of the quantum initial state for the highly anisotropic graphite crystal is discussed in detail as well as the dynamical consequences of energy redistribution during the scattering process. The graphite surface application demonstrates that the Boltzmann operator Wigner transform for a system with 900 degrees of freedom can be obtained by the so-called gradient implementation [Poulsen et al. J. Chem. Theory Comput. 2006, 2, 1482] of the underlying Feynman-Kleinert effective frequency theory, an implementation that only requires a force and potential routine for the system at hand, and hence is applicable to any molecule-surface collision problem.