Time-delay signature (TDS) suppression of an external-cavity semiconductor laser (ECSL) is important for chaos-based applications and has been widely studied in the literature. In this paper, the chaotic output of an ECSL is injected into a semiconductor laser and TDS suppression in the regenerated time series is revisited. The focus of the current work is the influence of parameter mismatch on the TDS evolution, which is investigated experimentally and compared systematically to simulations. The experimental results demonstrate that it is much easier to achieve desired TDS suppression in the configuration composed of mismatched laser pairs. Numerical simulations confirm the validity of the experimental results. In the experiments and simulations, the influence of the injection parameters on TDS suppression is also studied and good agreement is obtained.