Binary black holes emit gravitational waves as they inspiral towards coalescence. Searches for electromagnetic counterparts to these gravitational waves rely on looking for common sources producing both signals. In this paper, we take a different approach: we investigate the impact of radiation zone effects, including retardation effects and gravitational wave propagation onto the circumbinary disk around stellar-mass, spinning black holes, using general relativistic hydrodynamical simulations. Then we used a general relativistic ray-tracing code to extract its X-ray spectrum and lightcurve. This allowed us to show that radiation zone effects leave an imprint onto the disk, leading to quasi-periodic patterns in the X-ray lightcurve. The amplitude of the modulation is weak (<1%) but increases with time and is strongly dependent on the inclination angle.