Are you perhaps mis-applying how we say that photons carry the electromagnetic force?

If so, for now we believe that gravity is simply the result of the warping of spacetime, with no known carrying particle. That's kind of the hurdle between uniting gravity with the quantum world.

If say, it turns out that there is such a thing as a graviton - which carries gravity, then gravitational waves would be a bunch of gravitons.

The surface of water is warped by a rock thrown into a pond, but no rock is transmitted by the waves. The electromagnetic field is disturbed by accelerating charges but no charges are transmitted by the EM waves.

In any case, mass is not the only thing that warps spacetime. The components of the stress–energy tensor [1] include energy (which includes mass) density, energy flux, momentum density, and momentum flux, the latter of which is composed of pressure and shear stress components.

[1] https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor

You're essentially asking the same question after it's been answered. Space-time is the carrier that acts like a fabric, and some large cosmological mass is distorting that fabric.

The distortion of the fabric of space-time ripples throughout the entire universe at the speed of light, and spreads it's effect proportional to the inverse square related to distance.