Mensa Dresden does not communicate with any service aside from the Studentenwerk Dresden for loading current meal information and your Autoload transactions.
The app does collect basic anonymous usage stats (to see what languages and operating systems are in use and if certain features of the app are unnecessary) using Telemetry Deck (see their Privacy Policy) and data on crashes directly through Apple.
Your preferences, last Emeal scan data and autoload credentials, if available, are stored on device. The latter encrypted securely in your device's keychain.