Access you control; nothing posts unless you ask.
The app reads your Google data to check lessons and show your numbers, and only you can see your data in the app. It changes nothing on Google by itself: a review reply or Business Profile post goes out only when you press Post or schedule it (DIY Plus and Pro).
To disconnect, open My Business and press Disconnect Google on the Google connected card. You can also remove access anytime from your Google Account's security settings. Lessons that were already completed stay completed.
Related: Connecting Google