Using ensemble of N gravitons, we evaluate the integrated density of states for gravitons arising from the spiral-in motion of gravitationally bound neutron star (NS) binaries, under the Dirichlet boundary conditions. Consequently, the two massive objects making up of the binary system are immersed in a gravito-bosonic environment. The corrections to the density of states for gravitons give expression to the quantum fluctuations of gravitational fields, i.e., the gravitational Casimir energy. By considering the extended scales of the star components, we find the gravitational Casimir effects are larger than that obtained by treating them as point particles and that the gravitational Casimir energy depends both on the scales of objects and on the separation of the binary, which increases for lager scales of star components in a typical NS binary system, with separation of , i.e. low-frequency gravitational wave sources.