Deleted Aperture Library, Now Backup File in Its Place

Good evening,

I recently bumped the limit of storage on my Mid-2011 MacBook Pro (500GB) because of a large Aperture Library file (375GB). I've since moved the Aperture Library file to an external hard drive and deleted the original Library from my MacBook, but instead of leaving a nice, big amount unused space on my drive I now have a 'backup' section of the drive that equals the size of the file that I deleted. How do I remove the new 'backup' file so I have a that 375GB of space on my drive? A search for a .backups file on the drive reveals nothing... Please help.

Thanks,

E