Thomson-scattered photospheric light is the dominant constituent of the lower solar corona's spectral continuum viewed off-limb at optical wavelengths. Known as the K-corona, it is also linearly polarized. We investigate the possibility of using the a priori polarized characteristics of the K-corona, together with polarized emission lines, to measure and correct instrument-induced polarized crosstalk. First we derive the Stokes parameters of the Thomson scattering of unpolarized light in an irreducible spherical tensor formalism. This allows forward synthesis of the Thomson-scattered signal for the more complex scenario that includes symmetry-breaking features in the incident radiation field, which could limit the accuracy of our proposed technique. For this, we make use of an advanced 3D radiative magnetohydrodynamic coronal model. Together with synthesized polarized signals in the Fe xiii 10746 Å emission line, we find that an ad hoc correction of telescope- and instrument-induced polarization crosstalk is possible under the assumption of a nondepolarizing optical system.