  With the new measurements of $J/\psi$ and $\psi^\prime\to \gamma\eta_c \
(\gamma\eta_c^\prime)$ from CLEO and BES-III Collaboration, we re-investigate
the intermediate meson loop (IML) contributions to these radiative decays in
association with the quark model M1 transitions in an effective Lagrangian
approach. It shows that the "unquenched" effects due to the intermediate hadron
loops can be better quantified by the new data for $J/\psi\to \gamma\eta_c$.
Although the IML contributions are relatively small in $J/\psi\to
\gamma\eta_c$, they play a crucial role in $\psi^\prime\to \gamma\eta_c \
(\gamma\eta_c^\prime)$. A prediction for the IML contributions to
$\psi(3770)\to \gamma\eta_c \ (\gamma\eta_c^\prime)$ is made. Such "unquenched"
effects allow us to reach a coherent description of those three radiative
transitions, and gain some insights into the underlying dynamics.
