A blackhole traveling at near light speed is pretty darned close to the analogy of a massive object instantaneously disappearing, similar to fictional spaceships engaging their warp engines.
Of course, it's not actually disappearing, just moving, but the original point was about detecting sharp changes in the gravitational waves. A quick Google search tells me that gravitational wave red shifting is a thing, and I imagine that with blackholes it's a very important phenomenon and area of study. And I would guess that there can also be interesting second-order effects that such a blackhole's movements have on the propagation of gravitational and electromagnetic waves from other objects.
Of course, it's not actually disappearing, just moving, but the original point was about detecting sharp changes in the gravitational waves. A quick Google search tells me that gravitational wave red shifting is a thing, and I imagine that with blackholes it's a very important phenomenon and area of study. And I would guess that there can also be interesting second-order effects that such a blackhole's movements have on the propagation of gravitational and electromagnetic waves from other objects.