The Inverse Rayleigh distribution is frequently utilized in reliability and survival analysis. This study focuses on deriving modified maximum likelihood estimators for the scale parameter of the Inverse Rayleigh distribution under Type-II left and right censoring. The efficacy of the proposed estimators is assessed through comparison with Anderson-Darling, Kolmogorov-Smirnov, and Cramér-von Mises type estimators via Monte Carlo simulations across various censoring schemes and parameter configurations. Additionally, a numerical example is presented to illustrate the proposed methodology. The simulation study demonstrates that the proposed estimators outperform the others. Additionally, given their explicit nature, the proposed estimators can serve as initial values for obtaining the maximum likelihood estimator.