Permission: Media Manager Delete
The permission 'media-manager-delete', if present on your system will control which ProcessWire Admin users can trash or delete media in the Media Manager Library. The permission does not apply to media in the temporary folder pending review.
Please note that this permission is not created when the module is installed. To use it, you will have to create it first then assign it to a role(s) which in turn are assigned to users, in the normal ProcessWire way.