Spacetime is not a "thing" that can be bent or stretched, or have stiffness or elasticity, it is just geometry. We use the term "bent" regarding the path of objects through space-time but that is only by applying Euclidean Geometry, which actually does not apply. Objects, in the absence of other force, travel in straight lines in space-time, but these "straight lines" are more correctly called "geodesics" and are straight lines in Riemann Geometry (but bent in Euclidean Geometry) which is the correct math to describe space-time.
What they are talking about is a speculative model in which what we call "spacetime" is treated as if it were an elastic medium in order to investigate the implications of such a model. It is not something that can really be discussed at the "B" level and it is certainly not something that needs to be considered at all in order to understand the standard model of spacetime in General Relativity.I was reading this and they are talking about the stiffness of spacetime.