Othervise whole GR would collapce. Experimentally (but indirectly) measured value of speed of gravitational waves is c within 1% of experimental errors. Method of measurements - rate of lose energy by gravitational radiation in binary neutron star systems. Coincides with predicted by Gen Relativity value c with 1%.

All effects of GR (time dilation by gravity in GPS system, light bending, red shift, etc.) depend on the speed of propagation of gravitational disturbance, and if it is not c, all above observed effects would be off (GPS would not work, etc.).

Directly neither gravitational waves nor gravitons have not been detected (due to too rough tools we have).