sorry for the trouble, is it an ad in the bottom right corner of the desktop, or an update message promoting to update to PDF Architect 4 which only displays while running PDF Architect?
Tha latter can be disabled by disabling the automatic update check in help->options->general.
If there is also a "notification system" entry there, this will disable the desktop ads(this is the place to disable them in version 4).
The strange thing about this is to my knowledge the desktop ads were only introduced in PDF Architect 4, could you kindly send a screenshot of any of them to support(at)pdfforge(dot)org?
Or did you by chance install the free version of PDF Architect 4 parallel to PDF Architect 3?