Final answer:
The observer control option that should be used to ensure a very responsive mortar calls for fires during an offensive operation is Direct Control. This option allows for direct communication between the observer and the mortars, enabling immediate coordination and support.
Step-by-step explanation:
If the company commander wants the 1st plt FO team to be very responsive for mortar calls for fires during an offensive operation, the observer control option that should be used is Direct Control. In this control option, the observer is physically located with the firing unit and has direct communication with the mortars, allowing for immediate and precise coordination. This ensures a quick response and effective support during combat.