From phys.org and other sources

Well general relativity is non-linear in that if the equivalence principle(s)* is/are true then all forms of energy should, by having a mass equivalent per E/c², gravitate. Gravitational waves are a form of energy and thus ought influence each other as they pass by. But the coupling is comparatively weak ( gravity is the weakest known force ) so small amplitude waves should have a negligible effect on one other. It is only when you get to humungous mass densities that the wave-on-wave effects become significant. This is what is being added to the computer models here and thus ought better reflect the reality of black hole to black hole inspirals, collisions and ringdown. Presumably these adjustments might add features to the detected gravitational waves from such events.

I'm not sure that "how well this theory applies to the strange properties of black holes is still to be determined" is true. I thought it was done and dusted but I guess in the extreme field limit other candidate theories are worth proposing to then disambiguate with measurements^**.

{ One thing that is very specific to GR : when you solve the field equations you are in effect solving for the geometry of spacetime given some arrangement of mass/energy. This geometry can change with time eg. the formation of an event horizon. Other forces assume a constant spacetime structure. }

{ I think they are referring to the work done by the MPG/AEI in Potsdam here. }

Cheers, Mike.

* Two forms, the weak and the strong. The weak form : equivalence of gravitational and inertial mass. The strong form : GR manifolds in the small are Minkowskian aka like Special Relativity.

** But GR has to be the odds on favourite here, with all the validations that it has undergone with no contradicting phenomena to date.

( edit ) If you are familiar with some aspects of the equivalence principle(s) but remain confused, then this paper seems to sort out the mess quite well.