When Gaal Dornick was leaving Synnax, everyone knew that she was a mathematician who was going to Sterling University on Trantor (that's why they were avoiding her).
Given, being a mathematician was heretical on Synnax and Seer Church was killing Mathematicians and Gaal Dornick was an acolyte (even bigger betrayal), why did Seer Church allow Gaal Dornick to leave?
Talking about fear from Empire (a jumpship was right at the doorstep), its possibility seems null because prosecution of Mathematicians on Synnax was an open information on Trantor and yet Empire never intervened. Either Empire didn't care or it feared the religion (less likely because this religion didn't have 3 trillion followers like Luminist).