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 stars, 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 polarimetric observations of the nearly edge-on disk around the pre-main sequence M-type star GSC 07396-00759, taken with VLT/SPHERE IRDIS, 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 our observations to characterize the location and properties of the dust grains using the Henyey-Greenstein approximation of the polarized phase function and evaluate the strength of the stellar winds. Results. We find that the observations are best described by an extended and highly inclined disk ($i\approx 84.3\circ \pm 0.3$) with a dust distribution centered at a radius $r0\approx 107\pm 2$ au. The polarized phase function $S12$ is best reproduced by an anisotropic scattering factor $g\approx 0.6$ and small micron-sized dust grains with sizes $s>0.3\mu$m. We furthermore discuss some of the caveats of the approach and a degeneracy between the grain size and the porosity. Conclusions. Even though the radius of the disk may be over-estimated, our results 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. With the caveats in mind, 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 from the disk.