Ultrathin III-V solar cells with proper light management have become more attractive than their optically thick counterparts as they are less expensive and lightweight, can maintain photon absorption, and have high radiation tolerance for space-related applications. Comprehensive optical modeling efforts have provided pathways to improve device efficiency in ultrathin GaAs solar cells with light trapping structures. Usually, the absorption mechanism known as free-carrier absorption (FCA) is ignored in these models due to the ultrathin layers and the direct bandgap of GaAs. This manuscript reports the significance of considering FCA as a parasitic loss caused by the optical enhancement in highly doped non-active layers between the ultrathin solar cell and backside light trapping structures. We model FCA based on Drude theory in a p-type AlGaAs layer behind ultrathin GaAs solar cells with a planar mirror and cylindrical gratings. Our results show that, depending on the AlGaAs thickness and doping concentration, free carriers will absorb transmitted photons and reduce the backside reflectance, degrading the current and voltage output from ideal conditions. One example shows that for a 300 nm-thick GaAs solar cell, the Ag mirror's peak reflectance decreases nearly 12% when the AlGaAs back layer is 800 nm-thick at a doping concentration of 4x1019 cm-3. Notably, the cylindrical grating designs with 38.5%, 46.5%, and 64.9% AlGaAs coverage resulted in an absolute efficiency reduction of 0.6%, 1.8%, and 2.9% at a doping concentration of 4x1019 cm-3, respectively. This novel study demonstrates that FCA in non-active layers must be properly addressed in the device design to progress the efficiency of ultrathin III-V solar cells with light trapping structures.