Two paths.
Edit the same playlist in Spotify (or wherever it lives). PlaceProfile re-fetches your imported playlists periodically. Within a few hours of you adding or removing tracks at the source, your atmospheric fingerprint updates automatically.
Replace the playlist outright. On your venue dashboard, remove the existing playlist (the trash icon next to it) and import a new URL. The fingerprint recomputes from the new track set.
If you want a faster refresh than the periodic re-fetch, click Reimport on the playlist row to trigger one immediately.