In addition to the decrease in the vacuum due exclusively to the distance from the source of the gravitational wave, the gravitational wave undergoes an additional damping when it passes through matter (stars, planets, dust, gas, etc)
According to the book Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Steven Weinberg, (Wiley, NY, 1972), chapter "10 General-relativistic theory of small fluctuations", page 585, equation 15.10.42, there it says:
...the energy density $\tau_g^{00}$ of these gravitational waves decreases as
$$\tau_g^{00} \sim R^{-4} \cdot \boldsymbol{e}^{\boldsymbol{-}\dfrac{16\pi G}{c^2} \displaystyle \int \eta \ dt}$$
(NOTE: I have added $c^2$ to the original formula in the book, which is expressed in units c=1)
...The factor $R^{-4}$ is just what we should expect for the free expansion of any wave representing a massless particle. [Compare Eq. (15.1.23)] The extra factor in (15.10.41) tells us that gravitational waves in a viscous medium are absorbed at a rate
$$\Gamma_g=16\pi \dfrac G{c^2} \eta$$
$\eta=$ coefficient of shear viscosity of the traversed matter
The $R^{-4}$ term is identical to the term for photons (massless particles) in an expanding universe. The interesting term is the one that expresses the damping when passing through matter $\Gamma_g$
I have performed a dimensional analysis:
$[G]=M^{-1}L^3 T^{-2}$
$[c]=L T^{-1}$
$[\eta]=M L^{-1} T^{-1}$
Therefore:
$[\Gamma_g]=T^{-1}$
As can be seen, everything is dimensionally coherent.
We see that the theoretical mathematical damping is a negative exponential and that therefore, theoretically, the energy density is never zero, although we know that physically we can consider that it has extinguished to zero when its value is below the limit in which the approximations of the model carried out to obtain the expressions, cease to be fulfilled.
Arxiv articles on this topic:
Damping of gravitational waves by matter
The damping of gravitational waves in dust
Best regards.