This story is from Rav Aviner. I dare say it’s instructive.
Ha-Gaon Rav Avraham Dov Auerbach, Av Beit Din (Head of the Rabbinic Court) of Tiveria, once told me about an incident that occurred there in the past: it once happened that the “eruv” was damaged, but the Rav of Tiveria ruled that it was kosher. There was a great Torah scholar who lived there and he bumped into the Rav of the city after Shabbat. They talked, the Torah scholar walked him home, and then they sat and chatted some more. The Torah scholar said, “Let’s learn some Torah.” The Rav of the city obviously agreed. The Torah scholar took Massechet Eruvim and they learned. Suddenly, the Rav of the city said, “Oy va-voy! If so, I ruled incorrectly today!” The Torah scholar said, “It appears so.” The Rav of the city asked, “Did his honor announce in his shul not to carry on Shabbat?” “No,” he responded, “since carrying in this place is a rabbinic prohibition, but honoring a Torah scholar is a Torah mitzvah. I therefore did not say anything.”
Even if the Mara De-atra errs, you cannot proclaim that he has erred. You can argue gently and try to persuade him’