  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 ($i\approx 84.3\,^{\circ}\pm0.3$) with a dust distribution centered at a
radius $r_{0}\approx107\pm2$ au. The polarized phase function $S_{12}$ is best
reproduced by an anisotropic scattering factor $g\approx0.6$ and small
micron-sized dust grains with sizes $s>0.3\,\mathrm{\mu}$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.
