This makes little sense to me, unless you mean that as a gravitating body moves through spacetime it distorts spacetime; then something else must act on spacetime in order to restore it to its original, non-distorted, state. Is that what you are saying?
Correct you must force it back or if space is passive have a radiation effect.
Lets take any random point in our solar system it's gravitional distortion is based on the effect it feels from every point in the universe. Lets deal with that not from the really really distant ones but the close ones but the lets say from earth to sun like distances.
You know the calculation the sun is 8 minutes away at the speed of light from earth which is the speed of gravity theoretically. So lets take a point right angles either side of the suns position right now and 8 minutes at the speed of light away. The deformation is some value x. Now roll forward one second. The sun has moved as we were initially right angles (the shortest distance) the distance to us must have increased slightly and so the gravity must drop by a small amount delta so we have x - delta. The key point here that point must not only distort it must undistort somehow.
We are back to the exact same situation as electric charge there are exactly three options here
1. The object is radiating gravity and space is passive. So the gravity at any point in space is the sum of the gravitational radiation of all objects. That is how classic physics taught electromagnetism so you end up with gravity looking like that radiating from everything. You can even end up drawing pretty radiation field lines like you did in classic electromagnetics. Big objects radiate the attractive force more than little objects because they are bigger and we have our theory.
2. The object is passive and space has an energy that can be deformed in the presence of mass/energy but will return back to normal when it moves. We saw this with Quantum Field Theory that particles become viewed as just a disturbance in the field and so gravity would be just some disturbance in some field. Underpinning this idea however is the the distortion of the field is unnatural and the field is fighting to return it to uniformity as the distortion carries energy. Hence a little mass distorts a little way a big mass further, you get your proportionality. In QFT we even had resonant points that could persist for long periods because the resonant point stopped that force being seen and we called them "real particles" and "virtual particles" were decayed by that force. In Electromagnetics we call it back EMF or counter-EMF, the opposition to deform the field. You can't have a field of this type without a back pressure, think about why.
3. Some mix of the above two schemes. We didn't really discuss this with QFT but there could be some sort of mix of both effects. The whole idea called heralding, it's sort of like phone ahead or notify in advance. In QM there are quite a few things that can be setup to be heralded so you know they are going to happen but as you can imagine this would make gravity really complex. This is like hidden variables explaining QM.
So number one would be how Newtonian physics would work with things radiating attractive force. GR fits into two and Einstein realized he needed a pressure to push spacetime back so he introduced the cosmological constant AKA dark energy.
The story is well covered in
https://en.wikipedia.org/wiki/Cosmological_constant Einstein did it as the article says to "hold back gravity" and achieve a static universe.
