You can delete a table's shared reports only if you have full administrative permission for that table.
To delete a shared report:
In the table bar on any application page, click the table containing the report you want to copy. Within the menu that appears, select Customize --tablename-- table > Reports.
Within the list of reports, locate the report you want to remove and click its Delete button.
In the confirmation prompt that displays, click OK.
Note: When you delete a report, all subscriptions to that report are also deleted.