Does Threema save chats on iCloud?

In and of itself, Threema does not provide an option to save chats on iCloud. If, however, you have chosen to save device backups on iCloud, all app data, including Threema chats, will be stored on iCloud.

Neither is there a way for third-party apps like Threema to control this behavior, nor can such apps detect whether iCloud device backups are enabled or not. Even though apps can exclude individual files from backups, these files are excluded from all backups, also from encrypted iTunes backups. Therefore, we recommend to either create iTunes backups instead of iCloud backups or to exclude Threema if you must create iCloud backups.

Threema Work admins can use the MDM parameter th_disable_system_backups to prevent iCloud and iTunes from including Threema Work data in backups. As mentioned above, it is, however, not possible to only allow iTunes backups.

To learn more about security aspects of iCloud backups, please refer to this Apple article.