We perform the numerical equivalent of a phase sensitive experiment on doped $t-J$ ladders. We apply proximity effect fields with different complex phases at both ends of an open system and we study the transport of Cooper pairs. Measuring the response of the system and the induced Josephson current, Density Matrix Renormalization Group calculations show how, depending on the doping fraction, the rung-leg parity of the pair field changes from minus to plus as the density of holes is increased. We also study the pair charge stiffness, and we observe a supression of the superconductivity in the region where static stripes appear. We compare our results with predictions from bosonization and renormalization group analysis.