  We use the experimental limit on the interference of M1 and E2 multipoles in
the $\gamma$-decay of $^{57}$Fe to bound the time-reversal-violating
parity-conserving $\rho N N$ vertex. Our approach is a large-basis shell-model
calculation of the interference. We find an upper limit on the parameter
$\bar{g}_{\rho}$, the relative strength of the T-violating $\rho N N$ vertex,
of close to $10^{-2}$, a value similar to the best limits from other kinds of
experiments.
