In this paper we propose an inversion strategy for the analysis of spectropolarimetric measurements taken by Hinode in the quiet Sun. The Spectro-Polarimeter of the Solar Optical Telescope aboard Hinode records the Stokes spectra of the FeI line pair at 630.2nm with unprecendented angular resolution, high spectral resolution, and high sensitivity. We discuss the need to consider a local stray-light contamination to account for the effects of telescope diffraction. The strategy is applied to observations of a wide quiet Sun area at disk center. Using these data we examine the influence of noise and initial guess models in the inversion results. Our analysis yields the distributions of magnetic field strengths and stray-light factors. They show that quiet Sun internetwork regions consist mainly of hG fields with stray-light contamination of about 0.8.