I don’t think gravitational waves traveling at the speed of light is the same as the gravitational attraction being apparently felt faster than light travels.

I don’t know how you would measure gravitational waves without measuring gravitational attraction.

It’s not light that is “communicating” that attraction.

Nobody said it was. The “speed of light” isn’t about “light”. Gravity propagates at the same speed, aka “c.”

This Reddit discussion on r/AskPhysics might help clear up your misconceptions. Notably:

Just to clarify: when people talk about the speed of gravity, they mean the speed at which changes propagate. It’s the answer to questions like: if I take the Sun and wiggle it around, how long does it take for the Earth to feel the varitation in the force of gravity? And the answer is that changes in gravity travel at the speed of light.

But that’s not what you’re asking about. Whenever you’re close to the Earth, gravity is always acting on you: it’s not waiting until you step off a cliff, like in the Coyote and the Roadrunner. The very instant your foot is no longer on the ground, gravity will start to move it downwards. The only detail is that it takes some time for it to build up an appreciable speed, and this is what allows us to do stuff like jump over pits: if you’re fast enough, gravity won’t be able to accelerate you enough - but gravity is still there.

I get the sense that you’re thinking about the second scenario when objecting to the concept that gravity travels at the speed of light.