  We show that an induced $s$-wave harmonic in the superconducting gap of an
orthorhombic $d_{x^2-y^2}$ superconductor strongly affects the excitation
spectrum near a twinning plane. In particular, it yields bound states of zero
energy with areal density proportional to the relative weight of the $s$-wave
component. An unusual scattering process responsible for the thermal
conductivity across the twin boundary at low temperatures is also identified.
