  The Generalized Kerr-Schild Ansatz (GKSA) is a powerful tool for constructing
exact solutions in Double Field Theory (DFT). In this paper we focus in the
heterotic formulation of DFT, considering up to four-derivative terms in the
action principle, while the field content is perturbed by the GKSA. We study
the inclusion of the generalized version of the Green-Schwarz mechanism to this
setup, in order to reproduce the low energy effective heterotic supergravity
upon parametrization. This formalism reproduces higher-derivative heterotic
background solutions perturbed by a pair of null vectors. Then we study
higher-derivative contributions to the classical double copy structure. We use
an orthogonality condition between the null vectors to impose linear
perturbations on the metric and the b-field. We reproduce higher-derivative
solutions for the gravity equations in terms of a pair of U(1) gauge vectors in
agreement with the KLT relation for heterotic string theory.
