H₀ posteriors obtained from multiple realizations of a double-image BBH lensing system with a true SIE mass profile. Gray curves show the posterior from each individual realization, while the sky-blue (N = 10), blue (N = 20), and navy (N = 30) curves represent the progressively combined posteriors. The dashed red lines indicate the true value of H₀. The top, middle, and bottom panels correspond to the cases of no delensing, SIS delensing, and delensing with the correct SIE model, respectively. In the absence of delensing, the inferred H₀ is strongly biased for all realization numbers. When delensing is performed with an incorrect SIS model, the bias is less apparent for a small number of realizations but becomes increasingly significant as realizations accumulate, even though the credible intervals shrink. In contrast, delensing with the correct SIE model recovers an unbiased estimate of H₀.