I am familiar with the setup he helped you design. I would advise not trying to remove those buttons. You will cause more trouble than its worth.
Do you use the Entity Search screen? Or are all of those Tables?
Ok so if I am reading this correctly the only Entity type linked to a screen is Deliveries? So Take Away and Pickup are not linked to a screen correct?
EDIT: Ok I see what your doing. You have 3 different departments for this?
The buttons are greyed out because there is no Entity Screen linked to them. The only one you linked was Deliveries.