By employing summary statistics obtained from Persistent Homology (PH), we investigate the influence of Redshift Space Distortions (RSD) on the topology of excursion sets formed through the super-level filtration method applied to three-dimensional matter density fields. The synthetic fields simulated by the Quijote suite in both real and redshift spaces are smoothed by accounting for the Gaussian smoothing function with different scales. The RSD leads a tendency for clusters (β₀) to shift toward higher thresholds, while filament loops (β₁) and cosmic voids (β₂) migrate toward lower thresholds. Notably, β₂ exhibits greater sensitivity to RSD compared to clusters and independent loops. As the smoothing scales increase, the amplitude of the reduced Betti number curve (β_k) decreases, and the corresponding peak position shifts toward the mean threshold. Conversely, the amplitude of β_k remains almost unchanged with variations in redshift for z ∈ [0−3]. The analysis of persistent entropy and the overall abundance of k-holes indicates that the linear Kaiser effect plays a significant role compared to the nonlinear effect for R ≳ 30 Mpc h⁻¹ at z=0, whereas persistent entropy proves to be a reliable measure against nonlinear influences.