Low-carbon manufacturing is an inevitable way to achieve carbon neutrality. Further, implementing a carbon emission quota policy is an essential method for boosting the low-carbon transformation of the remanufacturing industry. Our study aims to improve the quality of remanufactured goods and promote the low-carbon, high-quality growth of the remanufacturing industry. Using a three-level supply chain comprising original equipment manufacturers (OEMs), independent remanufacturers (IRs), and retailers, we construct a game model with and without a government-implemented carbon emission quota policy. Subsequently, we examine the consequences of the carbon emission quota policy on product quality, sales, and price. We also determine the optimal range of carbon quota for governments to enforce carbon emission rewards and penalties to promote the low-carbon production of remanufacturing companies. By comparing the equilibrium results, we conclude that the carbon emission quota policy incentivizes IRs to upgrade the quality of remanufactured goods and expand production. Notably, when the carbon emission limit is less than the threshold, the policy significantly reduces the gross carbon emissions of OEMs and IRs. However, when the carbon emission limit is greater than the threshold, the effect on gross carbon emissions is negative. This study enriches the theoretical research on manufacturing and remanufacturing and provides decision support for governments to formulate a carbon emission quota policy. It also offers practical guidance for manufacturers and remanufacturers in making production decisions.