You are the "owner" of any content that appears in the My Content page of your Echo360 Library. You can delete this content if it is no longer needed.
DELETING MY CONTENT MEDIA IS PERMANENT- you cannot recover either the media or the class data associated with it.
Items appearing in the Shared with Me page of your library are not associated with any other data; you are seen simply as the recipient of these items. As such, deleting this content deletes only the media. Any other sharing or publishing done by the owner of this content is not affected.
For instructions on deleting Echo360 recordings, see the Echo360 article Deleting Content from the Instructor's Library.