  We study the discrete massless Gaussian Free Field on $\Z^d$, $d\geq2$, in
the presence of a disordered square-well potential supported on a finite strip
around zero. The disorder is introduced by reward/penalty interaction
coefficients, which are given by i.i.d. random variables. Under minimal
assumptions on the law of the environment, we prove that the quenched free
energy associated to this model exists in $\R^+$, is deterministic, and
strictly smaller than the annealed free energy whenever the latter is strictly
positive.
