The formation mechanism of tidal dwarf galaxies means they are expected to contain little or no dark matter. As such, they might be expected to be very sensitive to their environment. We investigate the impact of ram pressure on tidal dwarf galaxies in a parameter study, varying dwarf galaxy properties and ram pressures. We submit model tidal dwarf galaxies to wind-tunnel style tests using a toy ram pressure model. The effects of ram pressure are found to be substantial. If tidal dwarf galaxies have their gas stripped, they may be completely destroyed. Ram pressure drag causes acceleration of our dwarf galaxy models, and this further enhances stellar losses. The dragging can also cause stars to lie in a low surface brightness stellar stream that points in the opposite direction to the stripped gas, in a manner distinctive from tidal streams. We investigate the effects of ram pressure on surface density profiles, the dynamics of the stars, and discuss the consequences for dynamical mass measurements.