We study a dual-channel recycling closed-loop supply chain (CLSC) and investigate the royalty strategy involving cost-reducing technique for remanufacturing patented products. Facing information asymmetry and market uncertainty, we address the problem where the patent licensor (manufacturer) and licensee (remanufacturer) simultaneously compete in the sales market and the recycling market. We examine the optimal decisions of a decentralized CLSC (D-CLSC) with the manufacturer being the Stackelberg leader. Numerical examples are used to demonstrate how the patented technology (cost-reducing technique) affects the channel players’ behaviors and how to identify the optimal royalty fee. Based on the theoretical derivation and the numerical outcomes, we find that regardless of the CLSC structure (centralized or decentralized), the take-back prices and the total profits will rise with the increase of savings from the licensed technology. In the D-CLSC, (i) the expected profits of the manufacturer and the remanufacturer as well as the royalty fee will also rise with the savings from the licensed technology. (ii) In addition, the wholesale price, retail price, take-back prices, as well as the royalty fee will rise with the degree of information asymmetry. But the retailer’s expected profit will decline. (iii) Finally, the expected profit of the manufacturer will rise with the demand uncertainty and the return uncertainty. For the remanufacturer, this trend is not obvious. Our research provides guidance to resolve conflicts and intellectual property disputes between the original manufacturer and the remanufacturer of the patented product.