FencepostErr1r: There are no doubt multiple ways of doing this, but how I would manage it is this: Before putting the stories in your device, give them a tag of some sort in Calibre ("sent-to-device", or whatever). As you finish them on your Kobo, delete them on the Kobo (go to the book in Library, long press, choose Delete).
Then when you re-connect your device to Calibre, view only the "sent-to-device" shelf. Sort them by clicking on the top of the "On Device" column. The ones that don't have a green tick on them are your Finished books. Then do whatever you want with them from there! (delete, archive, tag, whatever.)
It's quicker to do than it is to type out...
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