Recall the operant definition of "weird" here is something that fits into the sentence "I find the idea of 23% of the universe being invisible particles that we are completely incapable of detecting is weirder than the idea that we have gravity slightly wrong."
Mathematically, if we add non-linear terms to gravity, it isn't that weird that you might get a memory-like effect, among other things. But would someone who agrees with the previous sentence agree that this is still less "weird" than 23% of the universe being so invisible that we still can't pick it up, even in 2017?
That there's stuff that has a mass but doesn't interact well with light, or that space is able to curve itself without mass, thus also rendering Einstein false.
This immediately raises further questions: How long does space remember? How's the exact mechanism? Where and how does empty space store that information? What happens to E=mc2?
Clearly, Occam's Razor can only be applied correctly if you can distinguish what you really know from what are actually your assumptions. Not only do people hear what they want - but those who don't know don't know they don't know.
However, I get suspicious when someone argues by analogy. Your "my car remembers a crash, furthermore humans do remember, therefore space could also remember gravity" does not seem reasonable to me.
I am also not sure why my post got downvoted.
Edit: As I think about it, "but Einstein showed that you can bend space without mass" again is an argument by analogy. It doesn't matter what analogies exist. The theory should be tested according to empiric evidence. Pulling your analogies together judt for the sake of abandoning a different theory - where's the point in that?
Did you mean the metric tensor g_{\mu\nu} or the Ricci curvature tensor R_{\mu\nu}?
"Gravitational field" is one of those shifty things in GR that makes one sympathetic to MTW's refusal to identify the term with any particular mathematical object.
You're right though; there are plenty of exact solutions to the Einstein Field Equation which are vacuum solutions -- no matter, just gravity.
That's honestly not so "weird" at all. There are TONS of examples of objects and substances having that kind of behavior in nature. If I crash my car into something, the metal "remembers" what happened to it. If I run electricity through an inductor, the magnetic field "remembers" that electricity was being run through that space and doesn't just disappear the moment the electricity is turned off. Momentum is the same thing. Humans remember what happened to them because consciousness records everything that happens to us. What prevents gravity from being something similar? Gravity itself may mean exactly the same thing as space having a kind of memory and operating fundamentally by the law of cause and effect. Things may seem weird only in the absence of such a clear principle.