In the context of a globally interconnected recycling industry, unauthorized collection channels pose a significant challenge to the reverse supply chain management of electric vehicle (EV) batteries on a worldwide scale. Unauthorized recyclers disrupt end-of-life product collection, posing environmental threats. To address this issue, the adoption of blockchain technology and a reward-penalty system is considered, though it introduces potential drawbacks such as high costs and unintended information sharing. This study evaluates a supply chain involving a manufacturer, a retailer, an authorized recycler, and an unauthorized recycler. We investigate the impacts of the unauthorized recycler on battery recovery supply chain and the motivation of supply chain members to implement blockchain technology. The results highlight that the recycling prices, recycling quantities, and profits of the unauthorized recycler are higher than those of the authorized recycler. The fiercer the competition between the two recycling channels, the bigger the difference of recycling prices, quantities, and profits between the authorized and the unauthorized recycler. Reward and punishment mechanisms are ineffective in alleviating the problems caused by the unauthorized recycler. The manufacturer is inclined to share blockchain information with the unauthorized recycler, which reduces the willingness of the authorized recycler to implement blockchain technology.