Interstellar Boundary Explorer (IBEX) observations of the "ribbon" of enhanced energetic neutral atom (ENA) fluxes show that it is a persistent feature that approximately forms a circle in the sky, likely formed from secondary ENAs whose source lies outside the heliopause. The IBEX ribbon's geometry (radius and center) depends on ENA energy and is believed to be influenced by the draping of the ISMF and the latitudinal structure of the SW. In this study, we demonstrate that the ribbonʼs geometry also depends on the pitch-angle scattering rate of ions outside the heliopause, which we simulate under strong and weak-scattering limits. The ribbon radius in the weak-scattering model is ~4° larger than IBEX observations at most energies, and the strong-scattering model produces radii statistically consistent with IBEX at 1.1-2.7 keV. The simulated ribbon center is shifted between ~2° and 5° along the B-V plane away from the IBEX center for the weak and strong limits, respectively, suggesting that the pristine ISMF far from the heliosphere is shifted ~2°-5° away from our simulated ISMF toward the VLISM inflow direction. However, the magnitude needs to be decreased from ~3 to 2 μG for the weak-scattering model to be consistent with the IBEX ribbon radius, which seems unlikely. We also find that the presence of interstellar He does not significantly affect the ribbon in the strong-scattering limit but yields weaker agreement with data in the weak limit. Our results slightly favor the strong-scattering limit for the ribbonʼs origin.