Collective Thomson scattering (CTS) has the capabilities to measure phase space densities of fast ion populations in ITER resolved in configuration space, in velocity space, and in time. In the CTS system proposed for ITER, probing radiation at 60 GHz generated by two 1 MW gyrotrons is scattered in the plasma and collected by arrays of receivers. The transmission lines from the gyrotrons to the plasma and from the plasma to the receivers contain several quasioptical mirrors among other components. These are designed to produce astigmatic beam patterns in the plasma where the beam shapes will have a direct impact on the signal strength of the diagnostic, the spatial resolution, and the robustness of probe and receiver beam overlap against density excursions. The first mirror has a line of sight to the plasma and is thus exposed to severe neutron streaming. The present neutronics and thermomechanical modeling of a first mirror on the high field side indicates that the mirror curvature may warp due to heating. This may alter the beam quality, and therefore, thermal effects have to be accounted for during the design of the mirror. The modeling further demonstrates that thin mirrors are superior to thick mirrors from a thermomechanical point of view.