Remove an attached media from an article / project without deleting the media

Hi,

I’m going crazy with this issue :

When you insert a media into a post (article or project) they appear in the section “media uploaded to this article”.

Is there a way to remove the media, so that they wont appear in the page anymore, but without deleting them completely from the media library ?

If I click on delete on the right column, the media is deleted completely.
If I click on delete at the bottom, the media is just deleted from the selection.
If I click “modify” and then click on the cross of the media in the center window, it is also just removed from the selection.

Please help !! ??
Having to re-import entirely the media each time I need to simply remove it from an article is one of the most time-consuming activity !! Thanks !