Recent research has emphasized the benefits of accurately reconstructing the initial Lagrangian positions of biased tracers from their positions at a later time, to gain cosmological information. A weighted semi-discrete optimal transport algorithm can achieve the required accuracy, provided the late-time positions are known, with minimal information about the background cosmology. The algorithm's performance relies on knowing the masses of the biased tracers, and depends on how one models the distribution of the remaining mass that is not associated with these tracers. We demonstrate that simple models of the remaining mass result in accurate retrieval of the initial Lagrangian positions, which we quantify using pair statistics and the void probability function. This is true even if the input positions are affected by redshift-space distortions. The most sophisticated models assume that the masses of the tracers, and the amount and clustering of the missing mass are known; we show that the method is robust to realistic errors in the masses of the tracers and remains so as the model for the missing mass becomes increasingly crude.