In current remanufacturing supply chains, whether the original equipment manufacturer (OEM) independently engages in remanufacturing or delegating (authorizing or outsourcing) to a third-party remanufacturer (TPR) is influenced by the government's differentiated carbon tax. However, our understanding of the factors influencing the optimal choice among the three remanufacturing strategies (i.e., self-remanufacturing, authorizing remanufacturing, and outsourcing remanufacturing) is fairly limited. In particular, little attention has been paid to differentiated carbon taxes, which involve the government imposing a high carbon tax on new products and a low carbon tax on remanufactured products. To fill these gaps, this study develops game models that include an OEM and a TPR. Our analysis reveals four main findings. First, with the increase in carbon tax on new products, the price of both new and remanufactured products rises. By contrast, once the carbon tax on remanufactured products increases, only the price of remanufactured products rises. Second, when the carbon tax gap between new and remanufactured products is small and the ratio of environmental impact per unit of remanufactured products to that of new products is less than consumer preference, both outsourcing remanufacturing and self-remanufacturing could achieve a win-win situation in reducing environmental impact and enhancing consumer surplus. Third, regardless of the governments' setting of the differentiated carbon tax, the OEM, as a profit-seeker, will decline the authorizing remanufacturing to expand profits in any case. Further, when the carbon tax gap between new and remanufactured products is less than a certain threshold, the optimal mode for the OEM is outsourcing remanufacturing, followed by self-remanufacturing. Fourth, our numerical analysis indicates that the carbon tax gap between new and remanufactured products plays a vital role in optimal remanufacturing strategy selection. Notably, both the recycling scale of wasted products and consumer preferences for remanufactured products should be taken into account when making an optimal remanufacturing selection.