General Relativity is a local theory concerned with the mechanisms that generate the metric, the geodesics implied by the metric, and the coupling of objects to those geodesics.
The relevant forces are those which accelerate objects into non-geodesic motion (or boost them from one geodesic to another). Those are local[1] as well: electromagnetism and the nuclear interactions. There's nothing like a luminiferous aether or underlying medium in the Standard Model, even if you look funnily at the gauge bosons -- they obey Lorentz covariance.
I made a couple of sibling comments to yours, one of which deals directly with your comment's parent's idea of a gravitational aether.
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[1] RM Wald, _Quantum Field Theory on Curved Spacetime and Black Hole Thermodynamics_ (University of Chicago Press, 1994). Cf. the top of page 6 of Hollands & Wald 2014, https://arxiv.org/abs/1401.2026