Although coordinated direct and relay transmission (CDRT) using device-to-device (D2D) and non-orthogonal multiple access (NOMA) can enhance spectral efficiency (SE) and coverage in future 6G networks, it faces challenges related to performance robustness and the SE limitations due to the duplicated transmission. To overcome these challenges, we propose a backscatter NOMA scheme for D2D-aided CDRT systems, where backscatter enables efficient D2D communication, while NOMA facilitates cellular CDRT transmission. We derive closed-form expressions for the SE of the proposed scheme. Simulations verify the correctness of the theoretical analysis and the effectiveness of the proposed scheme.