  Radiative transfer investigations of the solar Mg II h and k resonance lines
around 280~nm showed that, while their circular polarization (Stokes V) signals
arise from the Zeeman effect, the linear polarization profiles (Stokes Q and U)
are dominated by the scattering of anisotropic radiation and the Hanle and
magneto-optical (MO) effects. Using the unprecedented observations of the Mg II
and Mn I resonance lines obtained by the Chromospheric LAyer
Spectro-Polarimeter (CLASP2), here we investigate how the linear polarization
signals at different wavelengths (i.e., at the center, and at the near and far
wings of the k line) vary with the longitudinal component of the magnetic field
($B_{L}$) at their approximate height of formation. The $B_{L}$ is estimated
from the V signals in the aforementioned spectral lines. Particular attention
is given to the following quantities that are expected to be influenced by the
presence of magnetic fields through the Hanle and MO effects: the sign of the U
signals, the total linear polarization amplitude ($LP$) and its direction
($\chi$) with respect to a reference direction. We find that at the center and
near wings of the $k$ line, the behavior of these quantities is significantly
different in the observed quiet and plage regions, and that both $LP$ and
$\chi$ seem to depend on $B_{L}$. These observational results are indicative of
the operation of the Hanle effect
