Noodle avoids offending Think-Tank but at the same time he corrects his mistakes. How does he manage to do that?
Noodle manages to correct Think-Tank without offending him by using a highly diplomatic and respectful approach. He is well aware of Think-Tank's massive ego and fragile pride, so he never directly points out his mistakes.
Instead of saying Think-Tank is wrong, Noodle presents his corrections as his own insignificant bit of data or a cloudy piece of information twirling around in his head. By downplaying his own intelligence, he makes his suggestions seem trivial rather than a direct challenge to the Commander's authority.
Furthermore, Noodle always prefaces his corrections with respectful apologies and salutations. He uses phrases like "Please excuse me, your Brilliance" and "I beg your pardon" before offering the actual correction. This softens the blow and prevents Think-Tank from feeling disrespected.
Noodle also constantly flatters Think-Tank, praising his intellect and agreeing with his conclusions. This feeds the Commander's ego, making him receptive to Noodle's inputs.
Ultimately, this clever strategy allows Think-Tank to save face. He easily accepts Noodle's corrections and claims they were his "next point" anyway, ensuring the right information is used without any offense taken.
Explanation
Noodle's character demonstrates high emotional intelligence and diplomacy. He understands that Think-Tank is autocratic and vain, so direct confrontation would be dangerous and ineffective. By phrasing corrections as minor thoughts ('cloudy piece of information') and using formal respect ('Please excuse me, your Brilliance'), Noodle feeds Think-Tank's ego while subtly guiding him to the right conclusions. This allows Think-Tank to adopt the correct information while maintaining the illusion that he knew it all along ('That was my next point').