  Given an abstract Wiener space $(X,\gamma,H)$, we consider an open set
$O\subseteq X$ which satisfies certain smoothness and mean-curvature
conditions. We prove that the rescaled resolvent operator associated to the
Ornstein-Uhlenbeck operator with homogeneous Dirichlet boundary conditions on
$O$ is gradient contractive in $L^p(X,\gamma)$ for every $p\in(1,\infty)$. This
is the Gaussian counterpart of an analogous result for the rescaled resolvent
operator associated to the Laplace operator $\Delta$ in $L^p$ with respect to
the Lebesgue measure, $p\in[1,\infty)$, with homogeneous Dirichlet boundary
conditions on a bounded convex open set $O\subseteq \mathbb R^n$.
