In general relativity the curvature of spacetime is described by something called the metric tensor, $g_{ij}$, which describes how distances work at each point. The field equations tell how it changes from point to point.
When there is matter around it produces curvature, but the field equations also describe how this curvature spreads out in space outside the matter. This is because the equations are second order differential equations: the curvature cannot just stop at the surface of the matter even if the surface is sharp, but instead change smoothly in a way that obeys the equations (producing what we normally call gravitational fields). It turns out that the influence of matter declines with distance, so you could say that when you move away in space spacetime regains its less curved shape.
There is a wrinkle here: gravitational waves. There are solutions of the vacuum equations that describe ripples in spacetime that do not correspond to any mass present. So even infinitely far away from masses you could in principle encounter such waves that make spacetime curve a bit. Just like normal mass-induced curvature actual gravitational waves from merging black holes and similar events get weaker the further they travel (but the amplitude goes down as $1/r$ rather than the $1/r^2$ for gravitation).
So far I have described this in terms of reduced influence in space, but relativity theory doesn't regard space or time as different (there is a thing about the time component having a different sign in the metric tensor from the space ones, but let's ignore it). That means that the previous arguments also apply if you were to remove material objects (or yourself) from a place: their gravitational influence and waves would decline, and since one second is equivalent to $\sim 300,000$ kilometres this would be relatively fast unless we speak about very heavy objects with vast radii of gravitational influence.
But what is the "force" smoothing things? The feedback is basically geometrical: if things curve in one way in one direction the relations described by the vacuum equations will make them curve the opposite way in another direction (technically/informally, a zero Ricci tensor $R_{ij}=0$ means that the metric is a harmonic function $\Delta [g_{ij}]=0$). The typical "strength" of this (setting a distance scale) is set by the gravitational constant and the units we measure things in.