ThreeWatch works without the use of a third-party server. There is no data being sent to me or any other third parties. ThreeWatch establishes a connection to Threema's webservers, generates a random 16-digit-password and talks to no one but those very servers.
- a random alphanumeric 16-digit-password generated on first app launch
This is required to ensure you don't have to log in manually each time you restart your devices so the app logs in for you automatically.
- a cache of 1-20 chats' information such as chat title, chat id and their last message
This enables the app to display the previous chat data during the time it connects to get the new chats.
As no data is being stored externally and all data stays on your iPhone and your Watch, simply uninstalling the app will remove the reference between the app and its data.
Basically, no one but you and your chat partner(s) you send those messages to. For more info on how Threema's encryption works, please refer to their documentation. For information regarding the connection between your iPhone and your Watch, refer to Apple's documentation (it's also really safe from what I can tell).