The data-driven inversion-based control (D-2-IBC) approach is a recently introduced control design method for uncertain nonlinear systems, relying on a two degree-of-freedom architecture, with a nonlinear controller and a linear controller running in parallel. Unlike other approaches for nonlinear control. D-2-IBC does not require an accurate modeling of the plant and is computationally efficient. In this paper, we introduce a finite-gain stability sufficient condition for the closed-loop system and prove that such a condition theoretically holds when a suitable constraint is enforced during the controller design. Finally, we compare the original and the modified methods on a benchmark simulation example, regarding control of the Duffing oscillator.