Which Role gives users the UI Action bar for Related Lists?

[Stephen Jenkins]

Hi, I need to provide a user with the ability to close Tasks within the REQ.  Just to be clear on what exact element i'm talking about I have circled it in the following screengrab from my end.  What role provides this actions menu in the related list view?

[Ankur Bawiskar]

@Stephen Jenkins 

catalog tasks are usually closed via UI action on sc_task form and not from related list.

Did you check that user has write access to table level? Did you debug security rules?