A semi-infinite space Green's function of the time-dependent radiative transfer equation is derived based upon an exact solution for anisotropic scattering in infinite space and the approximated extrapolated boundary condition. The obtained solution is compared to Monte Carlo simulations and used for retrieving the optical parameters of simulated data in a nonlinear fit. It is shown that the solution performs well for boundaries with mismatched refractive indices. The relative errors in the fitted optical parameters are considerably smaller than by using the diffusion theory.