ABSTRACT The afterglows to gamma-ray bursts (GRBs) are due to synchrotron emission from shocks generated as an ultrarelativistic 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 ∼100 Mpc, the system should be inclined ≲20° for the reverse shock to be observable at ∼0.1–10 d 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.