How can “nothing” be warped?
It can't be. There's nothing to warp. However...
It is said that space is empty, a void, a “nothingness.” Space is the lack of anything.
Who said that? Einstein didn't. Einstein said space was neither homogeneous nor isotropic where a gravitational field was. He said this:
"This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials guv), has, I think, finally disposed of the view that space is physically empty."
He said space isn't nothing. It's a thing, not a nothing, something that is conditioned by energy in the guise of a massive star, this effect diminishing with distance.
And, Einstein showed that “gravity” is the warping of spacetime.
He didn't actually say that. Try finding where he said that. You won't be able to.
Objects with mass do not “attract” each other; they tend to move toward each other because their masses warp the spacetime between them.
That's the popscience version I'm afraid.
But, if space is nothing, the absence of anything, then how can it be warped?
It isn't warped, it's rendered homogeneous. And it isn't nothing, it's something. See this Einstein article from 1929 where he talks about a field as a state of space:
"The two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric".
A gravitational field is one state of space, an electromagnetic field is another. Also note the Robert B. Laughlin quote here:
"It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed... About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids... Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness..."