To keep the label outlines from printing, go to the Layers tool and set it to not print or to not be visible. To see Adobe's recommendations, visit their Help site at https://helpx.adobe.com/support.html
Note: If you are using Adobe Reader and working with a PDF template, you probably won’t be able to make the borders not print. You need more advanced software for this. Instead, you can use Avery Design & Print Online.