Trunks takes a step back, after studying the doctor for a bit. Then puts his hands at his sides, and bows formally. Very like the Japanese from Earth. "I am sorry. For upsetting you, after intruding on your grief."

Even if he kind of wasn't sorry he'd come to find the other man, in some ways. Holding it for a moment, before moving to retrieve his sword and let the other have his privacy. He'll pick up and re-offer the handkerchief though.