You got it right.
Here's a simple thought experiment that will prove that gravity travels at the speed of light, or remarkably close to it.
Picture our solar system.
Picture a globe constructed of photographs of each of the planets in our solar system using the light that has come from them.
Picture a map constructed from the gravitational influences of each of these influences on the planet earth.
If gravity lagged behind light ... the oceans would not reach high-tide in the manner related by where the moon is in the sky. Neither would the gravitational influence of the sun on the earth and moon point back to the sun but rather to where the sun had been (past tense).
If gravity moved at a speed faster than light the opposite would be true. We would be pulled toward a location where visual observation indicated the sun had yet to move.
