Highly stretched hyperelastic membranes exhibit smooth surfaces during loading but develop wrinkles upon unloading due to the Mullins effect. Boundary curvature resists and suppresses these wrinkles beyond a critical threshold, maintaining smoothness throughout the loading-unloading cycle. This suggests a nonlinear interplay between Mullins and boundary effects in the entire cycle. Furthermore, the stress-strain response of PDMS films exhibits strain stiffening with a single turning point during uniaxial stretching, which the classical two-parameter Mooney-Rivlin (MR) model cannot adequately capture. To quantitatively reveal the underlying damage mechanisms, we develop a consistent finite-strain pseudo-elastic plate model based on the three-parameter MR model, incorporating two variables to account for stress softening and residual strain in rubber-like elastomers. This model accurately predicts the post-buckling morphological evolution. Results demonstrate three distinct morphological evolution patterns in highly stretched thin films. For films within a specific range of aspect ratios and boundary curvatures, no wrinkling during loading, but wrinkles upon unloading. For films with lower boundary curvature, wrinkles occur during both loading and unloading. For films with higher boundary curvatures, the film remains flat throughout the loading-unloading process. These findings establish a mechanistic competition between Mullins effect-induced wrinkling and boundary-suppressed instability, providing a theoretical foundation for designing tunable functional surfaces.