Ocean currents’ effect on long-range sound propagation, though considerable in many cases, is difficult to separate from much stronger effects due to sound speed inhomogeneities, as flow velocity is usually much smaller than typical variations in the sound speed. Dramatic improvement can be achieved in reciprocal transmission experiments when sound signals propagate in opposite directions between two transceivers (source–receiver pairs). The presence of a current results in the breaking of the principle of acoustic reciprocity, thus making it possible to use nonreciprocity of acoustic field as an indicator of water movement. In this paper, reciprocal acoustic transmissions through a submesoscale interthermocline lens of Mediterranean Water (meddy) in the Atlantic are considered theoretically as a possible tool for meddies detection. A simple model of acoustic ray-travel-time nonreciprocity due to a meddy is proposed. The analytic estimates obtained from the model show that the influence of rotary flow is more important than that of drift and seems to be measurable. The problem is studied in more detail via computer simulations. The environmental model used in the simulations corresponds to case studies performed in the Iberian Basin in 1989 and 1991. Numerical simulations show that travel times between two transceivers can be gathered into several groups; for the most part, rays in each set have similar geometry for both propagation directions. However, the lens strongly affects the number of rays in each group, their launch angles, and number of surface interactions, making it impossible to identify these arrivals as required for conventional ocean acoustic tomography. In spite of complexity of ray structure, travel-time nonreciprocity predicted by the model proposed is in good agreement with numerical results. This fact suggests that the model could be used to estimate some parameters of a meddy.