Graded TPMS topologies display excellent mechanical and thermal properties. Design schemes targeting optimal performance exist, but final reconstructed designs still suffer from performance degradation. To overcome this challenge, we propose an automated design framework based on the integration of a homogenization-based topology optimization scheme and a new mapping strategy. Optimized designs obtained using a modified SIMP technique are reconstructed as graded gyroid structures. Unlike mapping strategies using relative density values prior to TPMS infill, for the first time we make use of readily available adjoint sensitivities for mapping optimal densities to graded gyroid structures. Results show that the proposed framework delivers performance preserving graded designs when compared to original optimized designs obtained using OPTISTRUCT and superior performance in comparison to standard density-based mapping methods. The resulting graded design is manufactured using additive manufacturing and three-point bending tests are performed confirming simulation results and demonstrating the applicability of presented design scheme.