Is there a way to see if a macbook had a time machine backup done?
From what I'm gathering you want to see if anyone accessed your computer to make a backup of it. I found this thread which might answer your question for how to retrieve the time machine backup logs from your Mac. Run the following command in Terminal

log show --style syslog --predicate 'senderImagePath contains[cd] "TimeMachine"' --info


which will show the most recent backups made. There is one change needed since log files can show activity of another account, if your Mac doesn't have your log in trusted as an administrator, you need that permission to do the search. Just add sudo to the above command as shown below:

sudo log show --style syslog --predicate 'senderImagePath contains[cd] "TimeMachine"' --info