In the MARE experiment onboard the NASA Artemis 1 mission of the ORION spacecraft to lunar orbit, two anthropomorphic female phantoms, equipped with a large number of active and passive radiation detectors were flown. Among the detectors were both LiF:Mg,Ti and LiF:Mg,Cu,P TL detectors as well as Al2O3:C OSL detectors. In order to correctly interpret the measured doses, the effective relative TL/OSL efficiency for cosmic radiation of these detectors was calculated by combining simulated radiation spectra for the cis-lunar space conditions with the efficiency functions based on experimental data for different ions and on a microdosimetric model.The obtained results show that for the ORION shielding conditions, the relative efficiency of LiF:Mg,Ti is close to unity (0.95), while the remaining detectors show somewhat smaller efficiency: 0.90 for Al2O3:C and (0.81-0.86) for LiF:Mg,Cu,P. The analysis of the influence of the shielding thickness on the relative TL/OSL efficiency revealed, that for low shielding conditions, the relative efficiency may be more significantly decreased, reaching values between 0.71 (LiF:Mg,Cu,P) and 0.85 (LiF:Mg,Ti) for 1 g/cm2.