Yes. A public Buda Session link points to the same ongoing Session, not a frozen copy from the moment you shared it. If you keep chatting in that Session, later messages and related artifacts may appear when someone reloads the public page. Read-only access does not mean the content is fixed, so do not add information there that link holders should not see.
For a fixed, reviewed portion, put the selected result into a separate document, image or exported file and share that after checking its contents. Alternatively, share a completed Session and stop using that Session; continue future work in a new private Session. The public Session page is not a selector for an arbitrary excerpt. You can switch the Session back to Private and check the link while signed out, but changing access cannot retract copies someone already saved.
We have recorded a time-point or selected-message snapshot-sharing request. The sharing guide covers the Public/Private controls. Do you want to show the whole work process or only the final result? The Chinese discussion covers the same distinction.