This article considers a batch solution to the multiobject tracking problem based on sets of trajectories. Specifically, we present two offline implementations of the trajectory Poisson multi-Bernoulli mixture (TPMBM) filter for batch data based on Markov chain Monte Carlo (MCMC) sampling of the data association hypotheses. In contrast to online TPMBM implementations, the proposed offline implementations solve a large-scale, multiscan data association problem across the entire time interval of interest, and therefore, they can fully exploit all the measurement information available. Furthermore, by leveraging the efficient hypothesis structure of TPMBM filters, the proposed implementations compare favorably with other MCMC-based multiobject tracking algorithms. Simulation results show that the TPMBM implementation using the Metropolis-Hastings algorithm presents state-of-the-art multiple trajectory estimation performance.