No, at the moment there’s no way to disable these messages, though you shouldn’t see any more for a while. We only recently introduced this mechanism (in Dorico 3.1 in January of this year), and normally the messages only appear to users running trial licenses, or every once in a while when running the free Dorico SE to invite you to upgrade to Dorico Elements. If you were running a full, permanent license for Dorico 3.1 you would have received a one-time notification of the availability of Dorico 3.5 some time in the first week following Dorico 3.5’s release, but it wouldn’t appear again. Many users clicked through from this announcement to purchase their Dorico 3.5 update, so at least some users found them useful.
The Olympus Choir Elements announcement is the one and only announcement that a Dorico 3.5 user running a full, permanent license would have received, and again, you should only see it once. Please let me know if that is not the case.