In a way, handing Celeste her father's blade was a way of evening the playing field. Not just for her, but for Gio as well.
She already knew that he relied on his hearing aids to hear. And no doubt she had something up her sleeve to male sure that she used the fact that he could not hear without the tiny devices to her full advantage when the time came.
So while Celeste studied her father's blade. Holding it with a reverence that most people saved for things that held great religious significance, or were thousands of years old. Gio took the time to study her. She was looking at the blade in the same way children looked at their fathers like they had hung the moon. Clearly lost in memory.
Rather than try to rush her, Gio let her be, and not just because it was an emotional moment. He taking note of all the little observations he was making, and filing them away for use when they finally got down to business.