I had assumed it was established that it was a palm print. There are times when I'm inclined to feel a little suspicious of Scipio's love of argument combined with, what I suspect is, a pathological NEED to be right 
Since I love to argue I can argue any side of any thing. As far as being right is concerned, who would intentionally choose a losing argument? Sometimes you get assigned a loser argument you are stuck making. When I pick my own I pick the ones best supported.
A) The lab failed to find any bloody fingerprints or palm prints on the Bible. They would be in the best position to know what it was
B) Sheila did not have any blood on her inside palm.
C) Nothing the killer did would result in getting the victim's blood over their entire palm. There was spatter but spatter doesn't coat a hand fully or anything else fully which is why the rifle stock wasn't completely covered the blood was sporadic
D) There was blood under the Bible corresponding to where that stain is and blood corresponding to where the blood on the left page stain is.
Look at how rounded the palm print is and the veins in it. The stain on the bible is not rounded and doesn't have veins. The only way a glove could make that kind of stain would be if the entire palm of the glove was covered in blood. If you shoot someone you are not going to get that much blood on your gloves unless you stuck it in a pool of blood first.
Palm prints from shootings are much smaller you only get a small section of the hand or a finger(s) not a big giant mass. Unless someone is suggesting Jeremy stuck his hand in a puddle of blood the suggestion doesn't work.
The COA adopted the prosecutions argument that the blood got there from being placed in the pool of blood I didn't think this up myself:
"
The more each member of the court looked at the photographs in order to deal with this point, the more difficult we found it to reconcile the actual bloodstaining with the defence case. The largest area of blood seems to have got onto the Bible when it came into contact with a pool of blood beside the body. As already observed the Bible must have been shut whilst the blood was wet. It does not seem very likely that it was still wet hours after the event when the police might have handled it. If this is so, it was shut by someone and then reopened to lie beside the body after Sheila Caffell had been shot. These matters along with other considerations of a similar kind were placed before us by the prosecution on an application to call fresh evidence with which we will deal later. It did not, however, require fresh evidence for us to see that there was a potentially powerful point that might have been made in this regard by the prosecution at trial."
The other fresh evidence they allude to is evidence that Sheila was shot while propped up against something then after she died was dragged flat to dump the rifle on her.
his evidence helps establish she was murdered. HOWEVER, it was not able to be used in the appeal for the purposes of proving such. There is no new science at play allowing the prosecution to make these arguments. The science and factual evidence existed at the time of the trial. They could have had experts argued about the Bible being placed in her blood after she was dead and being moved after she was dead. They failed to recognize these arguments and that is their touch luck. If there were a retrial they could raise such but can't raise such to defeat the need for a retrial.