The rapid proliferation of electric vehicles has led to a significant increase in the quantity of used electric vehicle batteries (EVBs). This necessitates the design of a waste reverse supply chain to reuse and recycle EVBs and protect the environment. This study examines an integrated reuse network design and pricing problem for EVBs. To design a reliable EVB reuse network to hedge against return quantity uncertainty, we present two bilevel globalized distributionally robust (GDR) design and pricing models. We derive computationally tractable reformulations of GDR expectation and chance constraints. For the resulting joint chance-constrained model, we propose a tailored branch-and-cut (B&C) algorithm and introduce a strengthened formulation to speed up the solution process. A real-world case study is conducted to validate the superiority of the proposed methods and examine the impacts of key model parameters on profitability. Results demonstrate that the globalized distributionally robust optimization models exhibit greater robustness than stochastic optimization models. The computational performance of the tailored B&C algorithm incorporating a strengthened formulation is assessed compared to the standard solver. Finally, based on the numerical results, we derive managerial insights from the analytical findings.