The on-chip integration of single photon and entangled photon emitters such as epitaxially grown semiconductor quantum dots into photonic frameworks is a rapidly evolving research field. GaAs quantum dots offer high purity and a high degree of entanglement due to, in part, exhibiting very small fine structure splitting along with short radiative lifetimes. Integrating strain-tunable quantum dots into nanostructures enhances the quantum optical fingerprint, i.e., radiative lifetimes and coupling of these sources, and allows for on-chip manipulation and routing of the generated quantum states of light. Efficient out-coupling of photons for off-chip processing and detection requires carefully engineered mesoscopic structures. Here, we present numerical studies of highly efficient grating couplers reaching up to over 90% transmission. A 2D Gaussian mode overlap of 83.39% for enhanced out-coupling of light from within strain-tunable photonic nanostructures for free-space transmission and single-mode fiber coupling is shown. The photon wavelength under consideration is 780 nm, corresponding to the emission from GaAs quantum dots resembling the 87Rb D2 line. The presented numerical study helps implement such sources for applications in complex quantum optical networks.