Just in case anyone else has this same question I found the answer. Once a file is uploaded to the server you can hide it in the Launch Center by;
- Open the file.
- Go to File -> Sharing -> Share with FileMaker Clients.
- In the FileMaker Network Settings box that appears check the box labeled "Don't Display in Launch Center".
While it makes sense now, I never thought to look there to hide a file that was located on the server. I thought that window was only for peer to peer settings.