The use of liquid fuel and the subsequent high fission product (FP) mobility are key features that distinguish molten salt reactors (MSRs) from other nuclear reactor designs. Among the potential advantages of MSRs, the possibilities of having online refueling and fuel reprocessing systems have been recognized as key design options. One of the online processes proposed for the liquid fuel is the extraction of fission gases (FGs), notably xenon and krypton, by a dedicated helium bubbling system. In this work, a multiphysics modeling tool is used to investigate the effect of the efficiency of a FG removal system on the FP concentration and distribution inside the liquid fuel of a small MSR concept. Additionally, a model of the migration of FG atoms dissolved in the salt to the circulating bubbles present in the system is described, and a parametric study is performed for the main variables affecting the mass transfer process: Sherwood number, Henry constant, diffusion coefficient, bubble diameter, and bubble volume fraction. The main objective of this study is to determine the impact of these parameters in order to select the most suitable modeling approach for capturing the relevant mass transfer phenomena and to provide an accurate description of the MSR removal system’s performance for different FGs. The analysis shows that a high removal efficiency is required if the goal of the helium bubbling system is to reduce the concentration of short-lived FGs and their daughters, which account for an important fraction of the total amount of FPs in the fuel circuit. Moreover, the half-lives of the FGs and the fraction of the FG inventory inside the bubbles were identified as the main parameters affecting the removal system’s efficiency. However, the results also indicate that the behavior of the FG daughters that are produced by radioactive decays inside the helium bubbles will require further detailed studies. These studies would have to consider the phenomena associated to the retention (or not) of the FG daughters at the bubbles’ gas-liquid interface. Finally, the results also confirm that in MSR systems, an accurate prediction of the FG removal efficiency requires the use of three-dimensional two-phase-flow simulations to accurately describe the bubbles’ distribution in the fuel salt and thus their interactions with FGs and the efficiency of the bubbles’ extraction device.