This article describes how to edit past session start and end times.
You can do this for any completed session or session type. Go to Learner -> Data & Reports and select the session you want to edit. Put in the new session start and end time.
The box will also show you the time of the earliest data point and the lastest data point for that session. You can change the session times to match the time the session started instead of the time that you started using Motivity.
If a session was left running across several days, you can edit the session start dates as well.