  We study the polarization-dependent electronic Raman response of untwinned
YBa$_2$Cu$_3$O$_{7-\delta}$ superconductors employing a tight-binding band
structure with anisotropic hopping matrix parameters and a superconducting gap
with a mixing of $d$- and s-wave symmetry. Using general arguments we find
screening terms in the $B^{\}_{1g}$ scattering channel which are required by
gauge invariance. As a result, we obtain a small but measurable softening of
the pair-breaking peak, whose position has been attributed for a long time to
twice the superconducting gap maximum. Furthermore, we predict
superconductivity-induced changes in the phonon line shapes that could provide
a way to detect the isotropic s-wave admixture to the superconducting gap.
