The composite structure of the Madden-Julian Oscillation (MJO) has long been known to feature pronounced Rossby gyres in the subtropical upper troposphere, whose existence can be interpreted as the forced response to convective heating anomalies in the presence of a subtropical westerly jet. Here we inquire as to whether these forced gyre circulations have any subsequent effects on divergence patterns in the tropics. A nonlinear spherical shallow water model is used to investigate how the introduction of different background jet profiles affects the model’s steady-state response to an imposed MJO-like thermal forcing. Results show that a stronger jet leads to a stronger Kelvin-mode response in the tropics up to a critical jet speed, along with stronger divergence anomalies in the vicinity of the forcing. To understand this behavior, additional calculations are performed in which a localized vorticity forcing is imposed in the extratropics, without any thermal forcing in the tropics. The response is once again seen to include pronounced equatorial Kelvin waves, provided the jet is of sufficient amplitude. A detailed analysis of the vorticity budget reveals that the zonal-mean zonal wind shear plays a key role in amplifying the Kelvin-mode divergent winds near the equator. These results help to explain why the MJO tends to be strongest during boreal winter when the Indo-Pacific jet is typically at its strongest.