We consider a hybrid manufacturing/remanufacturing system where the returned products (cores) are classified into different quality grades. Each grade requires different remanufacturing operations and thus lead times. We examine the implications of the quality-grading scheme on the dynamic behavior of closed-loop supply chains, benchmarking this against a typical system where all the returns undergo the same remanufacturing process. Through control engineering techniques, we evaluate the Bullwhip and inventory performance of the supply chain by observing the step response of the orders and net stocks (the shock lens), analyzing the frequency behavior of these signals (the filter lens), and measuring their dynamics due to stochastic demand (the variance lens). Subsequently, we discuss the operational savings and additional costs derived from quality grading. We find that the pre-sorting mechanism allows for smoothing the supply chain operations; however, its impact on customer satisfaction is ambivalent. Indeed, we observe that the documented ‘lead-time paradox’ of the remanufacturing process in hybrid systems results here in a ‘quality paradox’: lower quality returns may increase the performance of inventories. This affects particularly low-frequency demands. Importantly, we analytically derive the optimal setting of the closed-loop pipeline estimation in order-up-to policies for avoiding long-term inventory drifts. This analysis reveals key potential benefits of information transparency for improving the operational performance, and thus the environmental and economic sustainability, of closed-loop supply chains.