In the waste recycling Monte Carlo (WRMC) algorithm, (1) multiple trial states may be simultaneously generated and utilized during Monte Carlo moves to improve the statistical accuracy of the simulations, suggesting that such an algorithm may be well posed for implementation in parallel on graphics processing units (GPUs). In this paper, we implement two waste recycling Monte Carlo algorithms in CUDA (Compute Unified Device Architecture) using uniformly distributed random trial states and trial states based on displacement random-walk steps, and we test the methods on a methane-zeolite MFI framework system to evaluate their utility. We discuss the specific implementation details of the waste recycling GPU algorithm and compare the methods to other parallel algorithms optimized for the framework system. We analyze the relationship between the statistical accuracy of our simulations and the CUDA block size to determine the efficient allocation of the GPU hardware resources. We make comparisons between the GPU and the serial CPU Monte Carlo implementations to assess speedup over conventional microprocessors. Finally, we apply our optimized GPU algorithms to the important problem of determining free energy landscapes, in this case for molecular motion through the zeolite LTA.