Context. Broad, asymmetric, and red-skewed Fe K_α emission lines have been observed in the spectra of low-mass X-ray binaries hosting neutron stars (NSs) as a compact object. Because more than one model is able to describe these features, the explanation of where and how the red-skewed Fe lines are produced is still a matter of discussion. It is broadly accepted that the shape of the Fe K_α line is strongly determined by the special and general relativistic effects occurring in the innermost part of the accretion disk. In this relativistic framework, the Fe fluorescent lines are produced in the innermost part of the accretion disk by reflection of hard X-ray photons coming from the central source (corona and/or NS surface). We developed an alternative and nonrelativistic model, called the WINDLINE model, that is capable to describe the Fe line features. In this nonrelativistic framework, the line photons are produced at the bottom of a partly ionized outflow (wind) shell as a result of illumination by the continuum photons coming from the central source. In this model the red-skewness of the line profile is explained by repeated electron scattering of the photons in a diverging outflow. Aims. Examining the asymmetry of the fluorescent Fe K emission line evident in the XMM-Newton EPIC-pn spectra of the NS source GX 13+1, we aim to distinguish between the two line models. Because GX 13+1 is a well-known disk-wind source, it is a perfect target for testing the WINDLINE model and compare the spectral fits between the relativistic and nonrelativistic line models. Methods. We used two XMM-Newton EPIC-pn observations in which the Fe line profiles were previously reported in the literature. These observations are not strongly affected by pile-up, and the Fe emission lines appear very strong and red-skewed. In order to access the goodness of the fit and distinguish between the two line models, we used the run-test statistical method in addition to the canonical χ² statistical method. Results. The DISKLINE and WINDLINE models both fit the asymmetric Fe line well that is present in the XMM-Newton energy spectra of GX 13+1. From a statistical point of view, for the two observations we analyzed, the run-test was not able to distinguish between the two Fe line models, at 5% significance level.