We study a three-tier closed-loop supply chain in which a supplier sells un-remanufacturable key components to an original equipment manufacturer (OEM) and a third-party remanufacturer (TPR). The supplier has two options to price the key components: the uniform pricing policy and the differential pricing policy. Additionally, the OEM has the choice to either outsource or authorize the remanufacturing business to the TPR. Using a game-theoretic framework, we analyze the equilibria of multiple games that the two pricing policies and the two remanufacturing modes are available. Among other findings, we show that compared with the authorization remanufacturing mode, the outsourcing remanufacturing mode is a win-win solution for the supplier, the OEM, the consumers, and the society, but it may be detrimental to the TPR. Compared with the uniform pricing policy, the differential pricing policy may lead to win-win situation for the supplier, the TPR, and the consumers, but it hurts the OEM and the society. We also show that price discrimination can motivate remanufacturing and improve environmental benefits under certain conditions. The analysis of social welfare and environmental impacts provides timely managerial insights for governments considering relaxing anti-price discrimination laws. To check the robustness of our results, we extend our models to incorporate the production cost of key components, the remanufacturing cost, and a two-period framework. The results indicate that all core insights remain valid and the un-remanufacturability of key components hinders remanufacturing.