The documents still include the Paperpile links to ensure that we can always format the citations correctly and the bibliography contains Paperpile links so that (1) we can correctly identify it as a bibliography and safely replace it, and (2) make it easier for the author to get to the associated metadata when reviewing the bibliography.
You can export a copy of the document without any of these links by using the add-on. To open the add-on go to Add-ons --> Paperpile --> Manage Citations, in the Google Docs menu. Then in the sidebar click the gear and go to Export. Select the option to export the document with no citation codes. If you then save that exported copy as a PDF, it will not contain any links to Paperpile, and any URLs in the bibliography will correctly link to their external sources.