We consider an original equipment manufacturer (OEM) who faces competition from an independent remanufacturer (IR). The OEM decides the quality of the new product, which also determines the quality of the competing remanufactured product. The OEM and the IR then competitively determine their production quantities. We explicitly characterize how the OEM competes with the IR in equilibrium. Specifically, we show that the OEM relies more on quality as a strategic lever when it has a stronger competitive position (determined by the relative cost and value of new and remanufactured products), and in contrast it relies more heavily on limiting quantity of cores when it has a weaker competitive position. The IR's entry threat as well as its successful entry can decrease the consumer surplus. Furthermore, our results illustrate that ignoring the competition or the OEM's quality choice leads to overestimating benefits of remanufacturing for consumer and social welfare. In addition, we show an IR with either a sufficiently weak competitive position (so the OEM deters entry) or a sufficiently strong one (so the OEM is forced to limit quantity of cores) is desirable for reducing the environmental impact. Comparing our results with the benchmark in which the OEM remanufactures suggests that encouraging IRs to remanufacture in lieu of the OEMs may not benefit the environment. Furthermore, the benchmark illustrates that making remanufacturing more attractive improves the environmental impact when the remanufacturer is the OEM, while worsening it when remanufacturing is done by the IR.