Multi-junction solar cells allow to utilize sunlight more effectively than single junction solar cells. In our work, we present optical simulations of III-V-on-silicon solar cells with a metal grating at the back, which experimentally have reached more than 33% power conversion efficiency. First, we perform simulations with the finite element method and compare them with experimental data to validate our model. We find that accurately modeling the investigated geometrical structure is necessary for best agreement between simulation and experimental measurements. Then, we optimize the grating for maximized light trapping using a computationally efficient Bayesian optimization algorithm. The photo current density of the limiting silicon bottom cell is improved from 13.48 mA/cm2 for the experimental grating to 13.85 mA/cm2 for the optimized metal grating. Investigation of all geometrical optimization parameters of the grating (period, height, …) shows that the structure is most sensitive towards the period, a parameter highly controllable in manufacturing by inference lithography. The data is provided as a ZIP archive containing the raw simulation results from FEM calculations for the backside grating and TMM calculations for the planar front side as well as EQE and reflection measurements of the experimental cells used as a benchmark. Please refer to the readme file included in the archive for details about the data structure. Python code is supplied under DOI:10.5281/zenodo.5013230 that allows to generate the figures in the Optics Express publication “Optimizing metal grating back reflectors for III-V-on-silicon multijunction solar cells.” from the simulation raw data.