I was doing a bit more digging into this and I have a potentially better thought on the error:
DESCRIPTION: During restore restart, an I/O error occurred on checkpoint file '\\BackupServer\Folder\SQLBackupFolder\RestoreCheckpointDB7.CKP' (operating system error 5(Access is denied.)). The statement is proceeding but cannot be restarted. Ensure that a valid storage location exists for the checkpoint file.
I had to read that a few times to get a good idea as to what the problem was. So what it is saying is that it cannot create the chekpoint file. So I am not surprised that it errored.
What happens if you run this:
EXECUTE AS LOGIN = <SQL Server Agent Service account>
EXEC xp_cmdshell 'ECHO hello world > \\BackupServer\Folder\SQLBackupFolder\RestoreCheckpointDB7.CKP'
EXEC xp_cmdshell 'DEL \\BackupServer\Folder\SQLBackupFolder\RestoreCheckpointDB7.CKP'
I believe that the error is saying it cannot write the checkpoint file not that it can't read it. When the backup starts it makes a restore checkpoint file so if the restore gets interrupted you can continue from where it stopped. This file is what allows that. Since it cannot create it (for some reason), it gives you that warning but continues anyways as it can still do the restore, you just have to restart from the beginning in the event something interrupts the restore.
What the above script does is creates the file with the contents "hello world" in it and then tries to delete it. If you get any errors running the above code, it may not be re-runnable from the same session until you run the REVERT command.
EDIT - copy paste screwed up the SQL Command text. Fixed this
The above is all just my opinion on what you should do.
As with all advice you find on a random internet forum - you shouldn't blindly follow it. Always test on a test server to see if there is negative side effects before making changes to live!
I recommend you NEVER run "random code" you found online on any system you care about UNLESS you understand and can verify the code OR you don't care if the code trashes your system.