Considering the various things the Soldier has done and had done to it, this is probably not going to be a big deal, pain-wise. The only weird thing might be having someone's mouth on him. Because she absolutely just said bite. Ew. (But she's a handler. And the Soldier did promise. It can handle a little touching for the sake of helping Elena.)

"I heal quickly, it might not need the bandage," it says. Blood is usually drawn from the arm before or after missions, so that seems the most logical place for this, too. It rolls up its right sleeve, and offers her its arm. (The left, obviously, won't work. That there's made of metal.)