You cannot remove the Adobe watermark from an export of the Premiere Elements tryout, be it an export to file saved to the computer hard drive or a burn to disc.
But, you can remove the Adobe watermark from the Premiere Elements project file (known as the project.prel) after you purchase the program.
All you do is open the project file from the tryout in the purchase Premiere Elements and then....
a. In the opened project, go to Timeline Menu/and click on Delete Rendered Files
b. do nothing (some of us have found that the Adobe watermark automatically disappears from the tryout project file when that tryout project file in opened in the purchased Premiere Elements.
See which one works for you. The classical version of the how to is "a" above.
Looking forward to your results.