We design and fabricate a grating coupler for interfacing suspended silicon photonic membranes with free-space optics while being compatible with single-step lithography and etching in 220 nm silicon device layers. The grating coupler design simultaneously and explicitly targets both high transmission into a silicon waveguide and low reflection back into the waveguide by means of a combination of a two-dimensional shape-optimization step followed by a three-dimensional parameterized extrusion. The designed coupler has a transmission of −6.6 dB (21.8 %), a 3 dB bandwidth of 75 nm, and a reflection of −27 dB (0.2 %). We experimentally validate the design by fabricating and optically characterizing a set of devices that allow the subtraction of all other sources of transmission losses as well as the inference of back-reflections from Fabry-Pérot fringes, and we measure a transmission of 19 % ± 2 %, a bandwidth of 65 nm and a reflection of 1.0 % ± 0.8 %.