The visibility of the custom Copy and Move actions added to document libraries and lists, is controlled by the CopyMove feature XML files in the following folders on each Web front-end server:
C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\12\TEMPLATE\FEATURES\SPPCopyMoveSite
C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\12\TEMPLATE\FEATURES\SPPCopyMoveWebApp
By default, all users have access to the Copy operation while users need delete permission to access the Move operation. To hide CopyMove for all users but site collection administrators, add the following attribute to the <CustomAction> elements in the custom action XML files like DocLibActions.xml, PicLibActions.xml and CustomListActions.xml:
Rights="ManageWeb"
To hide CopyMove for all users but contributors, add the following attribute:
Rights="EditListItems,DeleteListItems"
Other possible values for the Rights attribute are defined by Microsoft here. However, the FullMask value will not work.
Finally, apply the changes by resetting the Web front-end servers with IISRESET.
WARNING! These changes are overwritten each time CopyMove is upgraded. Consequently, you should consider developing and deploying your own SharePoint feature with these changes. Use the CopyMove feature as a template for your own customized feature.