Context. One of the difficulties in extracting reliable information about the thermodynamical and magnetic properties of solar plasmas from spectropolarimetric observations is the presence of light dispersed inside the instruments, known as stray light. Aims: We aim to analyze quiet Sun observations after the spatial deconvolution of the data. We examine the validity of the deconvolution process with noisy data as we analyze the physical properties of quiet Sun magnetic elements. Methods: We used a regularization method that decouples the Stokes inversion from the deconvolution process, so that large maps can be quickly inverted without much additional computational burden. We applied the method on Hinode quiet Sun spectropolarimetric data. We examined the spatial and polarimetric properties of the deconvolved profiles, comparing them with the original data. After that, we inverted the Stokes profiles using the Stokes Inversion based on Response functions (SIR) code, which allow us to obtain the optical depth dependence of the atmospheric physical parameters. Results: The deconvolution process increases the contrast of continuum images and makes the magnetic structures sharper. The deconvolved Stokes I profiles reveal the presence of the Zeeman splitting while the Stokes V profiles significantly change their amplitude. The area and amplitude asymmetries of these profiles increase in absolute value after the deconvolution process. We inverted the original Stokes profiles from a magnetic element and found that the magnetic field intensity reproduces the overall behavior of theoretical magnetic flux tubes, that is, the magnetic field lines are vertical in the center of the structure and start to fan when we move far away from the center of the magnetic element. The magnetic field vector inferred from the deconvolved Stokes profiles also mimic a magnetic flux tube but in this case we found stronger field strengths and the gradients along the line-of-sight are larger for the magnetic field intensity and for its inclination. Moreover, the discontinuity between the magnetic and non magnetic environment in the flux tube gets sharper. Conclusions: The deconvolution process used in this paper reveals information that the smearing induced by the point spread function (PSF) of the telescope hides. Additionally, the deconvolution is done with a low computational load, making it appealing for its use on the analysis of large data sets. A copy of the IDL code is available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/579/A3