Drupal CMS - Find Content - how to drop the ?destination=admin/content in the edit link?
This is a result of the content editing screens returning the user to that. If they edit content from the front-end, the destination is the node.

You can override that default content manager with a View configured the way you want it. The 'Edit' link won't have a destination in the URL, and if I recall, it will return the user to the content after editing.

Also, if this is D6 and they have access to this page it sounds like they have administer nodes access. You might want to tune the permissions differently and setup a view so you can override admin/content path(s) with your View to override the content manager.