The short answer is that we store almost nothing - just student email addresses and names.
We designed Submit to store as little student data as possible. Students authenticate themselves using their school Google accounts and never need to create a Screencastify account. We grab student names and email addresses from the email account they signed in with.
Submit also temporarily stores student videos on Screencastify's servers while the videos are being processed and uploaded to the teacher's Google Drive. No student videos are stored on our servers for longer than 2 hours.