The afterglows to gamma-ray bursts (GRBs) are due to synchrotron emission from shocks generated as an ultra-relativistic outflow decelerates. A forward and a reverse shock will form, however, where emission from the forward shock is well studied as a potential counterpart to gravitational wave-detected neutron star mergers the reverse shock has been neglected. Here, we show how the reverse shock contributes to the afterglow from an off-axis and structured outflow. The off-axis reverse shock will appear as a brightening feature in the rising afterglow at radio frequencies. For bursts at $sim100$ Mpc, the system should be inclined $lesssim20^circ$ for the reverse shock to be observable at $sim0.1-10$ days post-merger. For structured outflows, enhancement of the reverse shock emission by a strong magnetic field within the outflow is required for the emission to dominate the afterglow at early times. Early radio photometry of the afterglow could reveal the presence of a strong magnetic field associated with the central engine.
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