Context. Debris disks have commonly been studied around intermediate-mass stars. Their intense radiation fields are believed to efficiently remove the small dust grains that are constantly replenished by collisions. For lower-mass central objects, in particular M stars, the dust removal mechanism needs to be further investigated given the much weaker radiation field produced by these objects. Aims. We present new observations of the nearly edge-on disk around the pre-main-sequence M-type star GSC 07396-00759, taken with VLT/SPHERE IRDIS in dual-beam polarimetric imaging mode, with the aim to better understand the morphology of the disk, its dust properties, and the star-disk interaction via the stellar mass-loss rate. Methods. We model the polarimetric observations to characterize the location and properties of the dust grains using the Henyey–Greenstein approximation of the polarized phase function. We use the estimated phase function to evaluate the strength of the stellar winds. Results. We find that the polarized light observations are best described by an extended and highly inclined disk ( i ≈ 84.3 ° ± 0.3) with a dust distribution centered at a radius r 0 ≈ 107 ± 2 au. Our modeling suggests an anisotropic scattering factor g ≈ 0.6 to best reproduce the polarized phase function S 12 . We also find that the phase function is reasonably well reproduced by small micron-sized dust grains with sizes s > 0.3μm. We discuss some of the caveats of the approach, mainly that our model probably does not fully recover the semimajor axis of the disk and that we cannot readily determine all dust properties due to a degeneracy between the grain size and the porosity. Conclusions. Even though the radius of the disk may be overestimated, our best-fit model not only reproduces the observations well but is also consistent with previous published data obtained in total intensity. Similarly to previous studies of debris disks, we suggest that using a given scattering theory might not be sufficient to fully explain key aspects, such as the shape of the phase function or the dust grain size. Taking into consideration the aforementioned caveats, we find that the average mass-loss rate of GSC 07396-00759 can be up to 500 times stronger than that of the Sun, supporting the idea that stellar winds from low-mass stars can evacuate small dust grains in an efficient way.