So, we know that when two objects of normal matter get away from each other, the gravitational pull they feel from each other, decreases.
I wanted to see how that would work. And in my over-simplistic understanding of physics, there could be two mechanisms that would create that phenomenon.
One is, simply, each body of mass stretches the fabric of space-time in a spherical fashion, relative to its mass, regardless of other bodies. Now, if another body of mass is in the vicinity, it would be pulled towards the first body, and also create the same effect for its own mass, so the first body would feel a pull too. If the second body moves away from the first one, it's moving out of the spherical pull, and its moving its own pull away, so the two bodies feel less gravitational pull.
The other mechanism would be somehow different. I should put it this way:
There is a certain amount of gravitational force in each body of mass. And all of that force gets "spent" on other bodies that have the force of the same type.
If there are only two bodies in the whole universe, their distance wouldn't affect the amount of pull they feel. But when there are other bodies around too (plus all the particles moving around), their distance would affect the gravitational pull that they feel from each other. But only because other "things" in the universe get a bigger "chance" of "catching" the gravitational force of those two bodies. Which means the force of those bodies get spent on other things around them, and less force remains to create pull between the first two bodies.
I don't know which one of those two explanations is closer to the current consensus on the workings of gravity, but to get an answer, I'd just simply ask:
If only two bodies of mass (earth and mars) make up the whole universe, and there is nothing around or between them (no photons or neutrinos or anything, hypothetically), would their distance affect how much pull they feel?
If you need more explanation:
Basic definitions of gravity (like $GmM/r^2$) only consider the mass of the two objects and their distance from each other as the playing factors in how much gravitational pull they feel. Based on those definitions, the answer to the question would be yes, obviously.
But are there other theories that would predict differently? If not, let's just assume that the answer to the question is "No, their distance wouldn't affect how much pull they feel." If so, are there any observations that would contradict this answer?