  We study cosmological gravitational waves generated during inflation under
the influence of a decaying cosmological "constant", in the
Transverse-Traceless (TT) gauge. In our approach we consider a non-perturbative
contribution of the dynamical cosmological "constant" to the tensor modes. As
an application of the model we study the well-known cases $\Lambda(t)=\sigma
H^2$ and $\Lambda(t) =\vartheta H$. The spectrum of gravitational waves for the
first case results scale invariant at the end of inflation, whereas for the
second case scale invariance is not achieved, leaving this to new proposals of
the form: $\Lambda(t)=f(H,H^2)$, in order to include inflation in some
$\Lambda(t)$CDM models. We also found that the non-perturbative contributions
of $\Lambda(t)$, accelerate the decreasing of the amplitude of gravitational
waves during a power-law inflationary stage, by an exponential factor.
