The file you need is in templates>portal>invoicepdf.tpl. There is another invoicepdf.tpl in your default template folder but I it is laid out differently than the PDF one from the portal folder.
Once you have this file opened, scroll to the bottom and you will see the $status variable. I changed my Unpaid RGB color to 255,255,255 instead of 204,0,0 so it is still there but unseen. This way I didn't have to mess around with any of the code any further though I may make some changes in the future.
Now that giant Unpaid doesn't show up anymore when I send PDFs.
hope this helps and I am sure there are other solutions.