The white dolphin was placed on the ground by the rattlesnake, and then Hawkeye and Jaguar started to treat the wounds urgently. They had done this many times before.
The temporary bandage was removed from the wound, and then the rattlesnake woke up the white dolphin. After the white dolphin woke up, the rattlesnake laid his flashlight horizontally in the white dolphin's mouth to prevent it from accidentally biting its own tongue while treating the wound later.
Given the sanitary conditions in the bat cave and the tools available in their hands, extracting the bullet would only hasten the white dolphin's death and was not particularly helpful. All they could do was disinfect the wound, stop the bleeding, dress it, and secure the joints surrounding the wound.
"The white dolphin has a lighter, Rattlesnake, find it," Jaguar told Rattlesnake.