Baki grows more serious at the first mention of trouble, his hands remaining unfolded as he settles back in, his eye narrowing. "I will expect to meet him at a later time, in that case." He begins, but for now he puts the third sibling aside to listen to Temari's explanation.

"...Mind transfer mishap...?" He repeats, almost incredulously. That is a lot to unpack in the space of a single phrase. Mind transfers weren't in his area of experience, but he had heard of them at least, enough to know some potential of what could affect Gaara. Honestly he hadn't actually thought such things were capable of affecting jinchūriki. "Who was in control of Gaara, then? Where was his mind transferred?"
The mention of keeping information from the Kazekage is accepted without Baki so much as batting an eyelash. He has long acknowledged the importance of keeping potentially compromising knowledge away from their father, as long as the safety of the village is not directly at stake. In that regard, he and his students have an understanding.