If you ask me to give you a rough estimate for the cost of the project, ___________ I would say thirty lakhs.

The preposition "Off-the-cuff" means without preparation or spontaneously, which fits perfectly with the phrase "a rough estimate."

"Off-the-mark" means inaccurate or incorrect, which doesn’t fit well grammatically or logically in this context.  "Off-the-grid" means not connected to public utilities or systems— not relevant here. " Off-the-mike" isn’t a standard phrase in English.

The correct answer is therefore Option A.