Well, you typically don't want public to have any permissions, other than perhaps read (we don't even want that), since, if anyone makes an ODBC connection to your databases, they'll have full access to read and write outside of JDE. So if you're like us, you'll want to remove all permissions.
You can do this either through the GUI (it would be a pretty arduous process when you are changing permissions in bulk) or through scripting. You do have to make sure that you've given the JDE user(s) necessary permissions before removing them from the public role, as by default, they are just inheriting whatever the public role has.
If you're new to SQL Server and don't have a DBA handy, I highly recommend reading about security and roles in the SQL Server Books Online. I could also send you the script we used to make the initial permission changes, but you're going to want to feel comfortable with the product before running such a script.