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Delete the rendered files for all projects.
Then check if the trial version message still comes.
Although that text will only disappear once you purchase and register the product too, of course.
Welcome to the forum.
This PrE FAQ Entry also covers the process of removing the watermark: http://forums.adobe.com/thread/433730?tstart=30
That will provide the instructions in one place for others, who might have the same question.
Just in case notes that may sometimes get overlooked.....
1. After purchase of the Premiere Elements, you can remove the Adobe watermark from a project file (project.prel) that you created during the tryout. But, you cannot remove the Adobe watermark that exists in one of the exports from the tryout project.prel file (even after you get a purchased serial number and are working from the purchased program).
a. The classical answer to getting rid of the Adobe watermark from your tryout project.prel files after you purchase the product is to delete the rendered files of the trial project.prel which is opened in the purchased program.
b. However, I and others have found the often just opening the trial project.prel into the purchased program removes the Adobe watermark automatically with no need to delete any rendered files.
See what works for you. Please let us know the outcome.