The magnetic fields in the solar polar region are important to our understanding of the internal dynamo process, the global coronal structure, and the origin of the solar wind. The inference of polar fields based on spectropolarimetric observation is highly model-dependent and can suffer from various systematic effects. Here, we analyze a raster map of the southern polar region taken by the Hinode Spectro-Polarimeter, utilizing the Stokes Inversion based on Response functions code. The inversions provide height-dependent vector magnetic field maps between optical depths log10τ=−2 and 0. We examine the impacts on the total magnetic flux estimates from adopting: (1) one-versus-two-component atmospheric models via a "filling factor" parameter; and (2) different analysis schemes. At log10τ=−1.5 , the polar magnetic flux is estimated to be (1.84 ± 0.03) × 1021 Mx and (1.38 ± 0.02) × 1021 Mx under the one- and two-component atmosphere assumptions, respectively. The magnetic flux is approximately constant or increases slightly with height, respectively. We find that the two-component (one-component) configuration is preferred for 58.3% (32.3%) of the pixels. Different initial guesses—including the input atmosphere model and the filling factor—as well as different inversion settings can significantly affect the results, especially for locations with weaker polarization signals. Our work highlights the importance of considering unresolved magnetic structures or stray light. Model degeneracy and the convergence to local minima limit the precision of the polar magnetic flux inference (no better than several tens of percent, in this case). Higher-resolution observations and advanced inversion and disambiguation algorithms may alleviate these limitations.