I'd recommend the folloging steps:
1. Get a text editor that supports search and replace for multiple files.
Under Windows I use Notepad++ for that purpose. It's free + open source (GPL).
2. Copy your entire /data directory and the .htaccess file from your gpEasy Installation
to a folder on your local computer.
Make a backup copy of this file/folder in case something goes wrong!
3. Open the .htaccess file
Perform a search and replace* in your .htaccess file and in all files in your /data subdirectory:
Replace /gpEasy/ with /
4. Copy/Overwrite .htaccess and /data/* in the gpEasy installation on your server.
Now everything should work.
(Keep your backup copies until you have checked your entire site!)
* In Notepad++ it's located in "Search" Menu -> "Find in Files". Check the checkboxes "Directory of the active file" and "Subdirectories"
Another note: I have tested a bunch of search and replace tools and quite a lot of them mess up the encoding of the files - which must remain UTF-8.
Notepad++ get's this right. If you use a different editor keep an eye on possible umlauts, diacritics and other non ASCII characters!