Well the pull of gravity is really just the warping of spacetime. A gravitational wave communicates the change in the gravitational field caused by an accelerat

Well the pull of gravity is really just the warping of spacetime. A gravitational wave communicates the change in the gravitational field caused by an accelerating mass. We measure this by shooting lasers along two paths and comparing how long it takes light to traverse the paths, the warping of spacetime causes this value to change. You could use this value to directly calculate how much the pull of the distant object upon us varied. But we can only see the variation, not the absolute pull, of these distant objects; and even then only for extreme cases like black hole and neutron star pairs moments before they collide.