Yes, you can.
To do this, click on the "..." icon and then on the "Delete" button.
If you delete a file from Media Center, it will be removed from all the places where it was attached (correspondence, profile, blog).
For example, if the deleted file is in the outgoing letter, the recipient will no longer be able to see it, and instead of the file there will be an inscription "this file has been deleted by the owner".
In other words, be extremely careful when deleting files from your Media Center, as this may affect your correspondence with other members of the site.