Gravity is the curvature of spacetime, and its effects travel at lightspeed. However, space is expanding; eventually, light from distant galaxies will become more and more redshifted, and we will no longer be able to see them (source).
As such, there is a limit to how far we could ever possibly see, since light too far will never reach us due to the rapid expansion of space...or at least, if I'm understanding this correctly.
Now, gravitational waves travel at lightspeed. So, after enough time, when an object's light no longer reaches us, will its gravity no longer affect us either?
A better rephrasing is: at a certain point in time, will the gravity of any extremely distant object — even the most massive stars, black holes, or galaxies — simply not affect us whatsoever, in the slightest?