No, mediteo and all its basic functions are free of charge. However, you can also purchase mediteo premium through an in-app purchase. Find out which features mediteo premium offers you and which subscription models are possible on https://www.mediteo.com/en/changes-to-mediteo-subscriptions/.
If you would like to support mediteo, you can do so within the app (“Profile” → “Subscriptions” → “Support mediteo”). This will give you access to a monthly PDF export of your health data for a certain period of time.