You know, it doesn't seem like much of a big deal at our point in time. But the sword was part of the Southern honor code, symbolic of defense of family, comrades and fellow warriors; it was also the mark of a true gentleman of a higher social class. Grant didn't wear one - it didn't mean that much for him. Asking for it would have been asking for submission, a humiliation of an already defeated foe - Grant didn't see any value in that, either. Lee should have offered it to Grant and it's a very interesting thing that tells one a good deal about Lee's real feelings there. At Cold Harbor, these two men had had an honor tug-of-war. Grant wanted Lee to ask for a truce to get the wounded, and Lee refused. He reminded Grant he'd gotten his men out - those were Grant's wounded. And why hadn't they been gotten yet...? Well, after a few exchanges Grant had to finally ask - he'd been licked, after all, not Lee!