Abstract <p> We derive the general cubic action for perturbations about a cosmological background in the quadratic subclass of degenerate higher-order scalar-tensor (DHOST) theories, focusing on scalar-scalar-tensor interactions. We adopt a fully covariant formulation and implement the unitary gauge at the level of perturbations. This mixed sector provides the key ingredient for estimating the decay rate of a gravitational wave into two scalar excitations in the quadratic DHOST models of dark energy in the late-time Universe. </p>