  We study the renormalization of a particular sector of Horndeski theory. In
particular, we focus on the nonminimal coupling of a scalar field to the
Gauss-Bonnet term and its kinetic coupling to the Einstein tensor. Adopting a
power expansion on the scalar function that couples the Gauss-Bonnet term, we
find specific conditions on their coefficients such that the action and charges
are finite. To accomplish the latter, we add a finite set of intrinsic boundary
terms. The contribution of the nonminimal coupling generates an effective
scalar mass, allowing us to recover a modified Breitenlohner-Freedman bound.
Furthermore, we compute the holographic 1-point functions and Ward identities
associated with the scalar field and the metric. We constrain the parameter
space of the theory by taking into account the preservation of scaling symmetry
at the boundary.
