Since the v6 redesign, Tinderbox only re-opens documents if the set to do so via the macOS System Settings. As at macOS 26.x, this is an option at OS System Settings ▸ Desktop & Dock section ▸ Close windows when quitting an application.
If needing to open Tinderbox without re-opening any documents open in the last app session, e.g. if a document gets corrupted or hangs, press the Shift key ( ⇧) whilst opening Tinderbox. This overrides the OS-wide option above.
Legacy
Pre-v6, Tinderbox had its own setting as to whether previously open documents were re-opened in a new session.