The title pretty much sums it up. We are running out of space on our backup disks, and need to remove old backups out of the set. I can't seem to find any information on this.
I would change your backup strategy to write to individual files for each database backup. You could then have a maintenance plan step that examines your backup location and removes *.bak files older the X days.
There's no way (that I've ever heard of) to delete a single backup from a backup file. This is why people write each backup to a separate file so you can just delete the old files.
Well, if you really want to get a db with those selected items you could restore the database to a new database and choose the backups you want to keep whilst restoring.