eBaymag lets you archive a listing. However, you don't delete it, but temporarily hide it from the list. So you have only actual listings on the Items page.
To archive listings, go to the Items page and tick them.
Then click the «Archive» button and confirm archiving.
To access archived listings:
Click the Filter button and select the Popular filter "Archived". Than click "Apply filters"
Now you should see only archived listings in the list.
To withdraw a listing from the archive, you should tick it and then click the "Unarchive" button.
If you decide to delete a listing, you cannot restore it anymore. All the cross-listings created in eBaymag will be deleted, but the original items will remain on eBay.
To delete listings, go to the Items page and tick them.
Then click the "Delete" button and confirm deletion.