This was one of the first link in the search results, so I'd figure I'd post to a stale topic.
In Layout, click on the component you want to hide the refdes. In the menustrip (File, Edit, View, ...), click Edit. Go down to the bottom and click Properties. If Properties is grayed out, you didn't select the component correctly. Click on the Markings tab. For the row 'RefDes' and column 'Show', change to 'Hide'.
Not sure why they made it such a pain. That properties option should be available when you right click a component.
I hope this helps all those searching and find this (stale) post.