There's no difference in the two types of behaviors you described. Your data is stored by google, and this app simply retrieves them and display to you. Since it doesn't store anything, it doesn't care if the task is deleted or checked off.
To retrieve, sync, submit changes, etc, this app communicates with the google server, and each month google allows the first x hits from this app (all users combined) to be free. That's how it works, but it's not something the user should worry about. The app has its own modal to estimate how "active" you are, but it's a very rough model.