Due to the limitations of technology and other aspects, outsourcing and licensing are the main forms of remanufacturing. This paper establishes a game model of remanufacturing supply chain between original manufacturers (OM) and third-party remanufacturers (3PR) with the participation of the carbon trading market, compares the equilibrium output, price, and profit under outsourcing and authorization models, and explores the impact of consumer recognition of remanufactured goods and the carbon emission rights trading price on the supply chain. The results show that: when the consumer’s recognition of remanufactured goods is low, the 3PR tends to authorize remanufacturing; otherwise, it tends to outsource the model; the OM tends to outsource remanufacturing when the profit is higher; the total carbon emission, consumer surplus and social welfare are higher under the outsourcing model. When consumer acceptance of remanufactured goods is higher, outsourcing remanufacturing is more beneficial to supply chain members and the environment. This study can provide theoretical basis for supply chain management decisions and reference suggestions for policy makers.