Geodesic curves are well suited for the design of elastic grid structures due to their straight development, which theoretically allows a flat strip to be bent onto any geodesic path without material strain. In practice, however, an elastically bent strip deforms into a state of minimal elastic energy rather than naturally adopting a geodesic configuration, causing spring-back effects and geometric deviations from the intended design surface. This paper proposes a novel inverse design framework for controlling the deformation of spatial geodesic strips through tailored incisions. By restricting the target shape to geodesic curves, the material frame aligns with the Darboux frame, reducing the inverse constitutive problem within Kirchhoff rod theory to two stiffness unknowns. The required stiffness distribution is computed from moment equilibrium under prescribed end loads and mapped to physical incisions through an explicit relation. The framework is validated through nonlinear finite element simulations across multiple spatial target configurations, demonstrating highly accurate results.