Navigate to the Backlink Manager section, then hover over the link that you'd like to modify until the ellipsis (…) appears on the right-hand side of the data. From the menu that appears, click the "Edit" button.

A window will appear displaying all current data for the backlink that you've selected. Modify any data field as you see fit. To move a backlink from Unpublished to Published status (or vice versa) simply change the status using the dropdown. Click "Save" to publish your changes.