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Grating couplers are important photonic devices on a complementary metal-oxide-semiconductor compatible silicon-on-insulator platform to couple light between optical waveguides and free space optical components or fibers. In this letter, we report the combination of a tilted grating coupler design, which strongly suppresses the back-reflection for light incident on the grating coupler from a waveguide, and a silicon overlay locally deposited on top of the grating region, which enhances the coupling efficiency of the grating coupler, by means of simulation and experiment. The fabricated tilted focusing grating couplers with silicon overlay show a coupling efficiency of -2.2 dB in combination with a back-reflection of around -40 dB when excited from the silicon waveguide. The tilted design also provides an alternative approach to enhance the transmission of a grating coupler when the thickness of the Si overlay is not optimized.