If gravity travels at the speed of light, and is affected by the local curvature of space, then logically it should be unable to have any remote effects since it could not escape..?
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There is a difference between gravity waves and gravitational waves – since you’re talking about black holes I assume you are asking about gravitational waves.
Gravitational waves are distortions in spacetime caused by massive objects accelerating sort of dragging spacetime with it causing ripples radiating outwards. A blackhole does not radiate (appreciable) gravitational waves unless it’s in a binary system with very short orbit close to merging.
Gravity waves are phenomena that oscillate under the influence of gravity like waves on a lake.
The reason nothing nothing can escape beyond a black holes event horizon is that spacetime is curved beyond the point where any path through it curves inward. Gravitational effects of this curvature of spacetime still exist beyond the event horizon because this is just another effect of it – gravity isn’t affected by the local curvature, it is the cause of it.
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