The full version won't remove watermarks from a video you have already made. You have to load the project file plus other source material into the full version of PE and re-make the video. No re-editing would be required.
As Allen points out, only the full-version can do this. Note that you MUST open the Project (created in the trial version) in the full-version. If you Export from the trial, you will have that watermark and it cannot be removed. Again, you will have to open the Project in the full-version, before you do any Export. Running the Exported AV in the full-version will NOT do it. Just a warning.