From what I have been able to glean off the internet, the 3rd was one of the early precursors to a modern day MASH unit. Portable surgical hospital teams consisted of an operating surgeon, two assistant operating surgeons, an anesthetist-internist, and up to four enlisted technicians. They were attached to clearing stations, field hospitals, and evacuation hospitals and performed procedures on patients in whom delay or transport would likely be fatal.
The 3rd had previously seen action in North Africa, Sicily and Italy, before being deployed to England in advance of Operation Overlord. I haven't been able to find out much about the unit, but what few facts I have located are presented below:
Of the Group's 18 portable surgical teams, 12 landed on Omaha Beach, while six landed at Utah Beach.
Two surgical teams from the 3rd accompanied the glider assault wave - their mission was to establish aid stations on the fields of the landing zone and to set-up an operating room for major surgical procedures.
A group of eight men from the 3rd also volunteered to go in on D-Day with the 101st Airborne Division - this detached service was an experiment to see if there was any advantage in taking a surgical team to where the casualties were, rather than transporting those casualties back to evacuation hospitals. The volunteers involved called themselves the 1st Airborne Surgical Team and they were attached to the 326th Airborne Medical Company.
Prior to the Battle of the Bulge, two surgical teams from the 3rd were sent to the 44th Evacuation Hospital in Malmedy, Belgium. Trucks carrying members of one of the teams passed through the main crossroads outside of Malmedy just minutes before German units took control of the intersection.
Dr. Norman Kornfield was a member of one of the 3rd's surgical teams. On December 22, 1944, in Liege, Belgium, Kornfield anesthetized the German officer who was thought to have ordered the Malmedy Massacre. Fifty years later, a newspaper article recounted Kornfield's experiences:
"...he needed blood badly. But blood supplies for Allied soldiers were scarce. I decided to just give him saline, and he died...an hour later, an American military intelligence team came to the hospital and asked to interrogate the captured German officer. Kornfield...regretfully told the intelligence team that the patient had died only an hour before. I could have saved him, Kornfield said. But the intelligence men told him not to regret his decision to withhold the needed blood. You did the right thing, Doc, one of the men said. We know everything we need to know about the Malmedy killings."
I am not quite sure what animal is depicted in this design and why it was chosen. it looks to me to possibly be a mole, but I'm not sure. I'm also not sure what type of medical instrument the animal is holding.
UPDATE: September 6, 2010
I now believe the animal in the image is a guinea pig, and the surgical instrument he is supposed to be holding in his hands is a scalpel.
Here is the image as it appeared in the April 1944 edition of Walt Disney's Comics & Stories: