Electromagnetic optimization is becoming increasingly important with the rise of high-tech applications, such as metalenses. Among the different topology optimization methods applied, a recent method combining level set optimization, parametrized with radial basis functions (RBFs), with enriched finite element analysis (e-FEA) offers promising results by creating smooth material edges without the need to remesh. Having these smooth material edges is crucial because the quality of the material edges has a significant impact on the performance of wave propagation designs. This method could help design metalenses for a number of different applications, such as improving the light-collection efficiency of scintillators. The method exhibited oscillatory behavior in the objective function in earlier wave-front-dependent designs, a phenomenon that has not yet been fully investigated. In this study, we analyze the dependence of the level-set optimization on the key parameters to optimize these parameters to reduce oscillatory behavior in the objective function and increase the performance of the final design. These parameters include the RBF radii, mesh sizes for the design and simulation mesh, initial level set hole seed, various methods for finding the location of the enriched nodes, regularization of the level set, and optimizer parameters. We provide a series of tests that analyze the impact of RBF parameters on the simulation and optimization of an electromagnetic design with a simulation test, shape-matching optimization, and electromagnetic identification problem. The results show that, although even large RBF radii can represent fine features in a design, this is not the case during optimization. Furthermore, an overfitted initial design variable field can also oscillate during the optimization. This formulation is then applied to a metalens optimization applied to a scintillator case. Without the optimized parameters, the results showed oscillatory behavior and a large dependence of the performance of the final design on the RBF parameters. Once the optimized parameters were implemented, the oscillations disappeared until the best design of the optimization was reached, and the performance was increased by 12.4%.