Hopefully I've explained what I want to achieve
Do you mean that you have lost the catalog and therefore have to import the images again? What rubbish will have to be deleted? Why not import only those images that you want to keep and delete the "rubbish" from Explorer/Finder without LR ever knowing of its existence?
Are you sure you have lost the catalog? What is backed up, the catalog or the image files? If you open a new catalog and reimport the images you will have lost any editing, keywording, rating, etc. that you did before. OTOH if you have backups of the catalog you can just copy the last one to your work drive and double-click it and you will be back in business.
You can't delete backup files that haven't been cataloged from within LR, but there are plenty of backup applications that will sync the two drives - i.e. delete from the backup drive (or a given folder) any files that aren't on the work drive.