My understanding was more that spacetime isn't perfectly elastic, so when it's distorted by a gravitational wave it stores the equivalent of a gravitational cha

My understanding was more that spacetime isn't perfectly elastic, so when it's distorted by a gravitational wave it stores the equivalent of a gravitational charge - a bit like a piezoelectric crystal that stays very slightly permanently polarised after you stop squeezing it. This would be amazing if true because spacetime would be rough on very tiny scales because of all the waves that passed through it. Speculating wildly, this might even have observable quantum-level effects.