While attempting to delete VM Templates from either vCenter Server's Content Library Section or from the vCenter Server Inventory, the delete operation fails with the message:
Task Name: Delete Library ItemTarge: VM NameStatus: The operation is not supported on the object.
The objects have already been deleted from the backing datastore, and therefore there is nothing to delete from the vCenter Server's perspective.
Delete the VM Templates from vCenter inventory using "Remove from inventory" option.
Note: If the Remove from Inventory option is greyed out (disabled), ensure there are no active tasks, such as a hung "Delete" or "Sync" operation, associated with the object. You may also need to check for file-level locks on the datastore if the host is still attempting to access the metadata Error Operation Not Supported.