What is this Google Backup and Sync "Back up your files" dialog asking?
Yes, you can have no "Boot OS X" folder now, but if you backup these files to cloud, there will be such a folder containing these files.
The most probably cause of this dialog is due to the update from old Google Drive to new Backup and Sync changed your source settings automatically though you didn't do by yourself. Thus, better check out your current settings to find out. If it is what i guess, then uncheck the related source folder will terminate such dialog.
Best wishes!