Radiative transfer investigations of the solar Mg II h and k resonance lines around 280 nm have shown 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 (χ) 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 χ seem to depend on B L . These observational results are indicative of the operation of the Hanle effect at the center of the k line and of the MO effects at the near wings of the k line.