I propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals based on GMM estimators even when the model is misspecified. In addition, my bootstrap does not require recentering the moment function, which has been considered as critical for GMM. Regardless of model misspecification, the proposed bootstrap achieves the same sharp magnitude of refinements as the conventional bootstrap methods which establish asymptotic refinements by recentering in the absence of misspecification. The key idea is to link the misspecified bootstrap moment condition to the large sample theory of GMM under misspecification of Hall and Inoue (2003). Two examples are provided: Combining data sets and invalid instrumental variables.