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The isovector time-reversal- and parity-violating pion-nucleon coupling$\bar{g}_{\pi}^{(1)}$ is uniquely sensitive to dimension six interactionsbetween right-handed light quarks and the Standard Model Higgs doublet thatnaturally arises in left-right symmetric models. Recent work has used the$\bar{g}_{\pi}^{(1)}$-induced one-loop contribution to the neutron electricdipole moment $d_n$, together with the present experimental $d_n$ bound, toconstrain the CP-violating parameters of the left-right symmetric model. Weshow that this and related analyses are based on an earlier meson theory $d_n$computation that is not consistent with the power-counting appropriate for aneffective field theory. We repeat the one-loop calculation using heavy baryonchiral perturbation theory and find that the resulting $d_n$ sensitivity to$\bar{g}_{\pi}^{(1)}$ is suppressed, implying more relaxed constraints on theparameter space of the left-right symmetric model. Assuming no cancellationsbetween this loop contribution and other contributions, such as the leadingorder EDM low-energy constant, the present limit on $d_n$ implies$|\bar{g}_{\pi}^{(1)}| \lesssim 1.1\times 10^{-10}$.

Nucleon Electric Dipole Moments and the Isovector Parity- and Time-Reversal-Odd Pion-Nucleon Coupling