What version of Premiere Elements are you using and on what computer operating system is it running? Since you mention trial version, that is probably Premiere Elements 12. Just asking in case any forthcoming post will require computer specific information in the reply.
Adobe watermark cannot be removed from the export of the Premiere Elements tryout, be the export a burn to disc product or a file saved to the computer hard drive.
But, you can remove the Adobe watermark from tryout Premiere Elements project files (project.prel) once you have purchased the product. To do that, you open the project.prel from the tryout in the purchased program and classically you go to Timeline Menu/Delete Rendered Files. For some of us, including myself, the Adobe watermark disappeared by just opening it in the purchased product. See which way works for you.
If you have been there and done that and the Adobe watermark issue remains, please let us know.