OHBowhunter, you misread my post. I actually more or less agreed with your approach, with the add-on that I would later tell the landowner what I did (sometimes easier to ask for forgiveness than permission approach). I was getting on BMRob because he was actually hunting on someone else's land without their permission and then hiding from them when they came onto their land. THAT is very different than the situation that started this thread. It is also different from someone landing a helicopter on your land or driving a car into your driveway or wearing clothes when walking on your land. Those were all personal belongings that were already the other person's property before they entered your property.
GMMAT makes an interesting point. Deer are a natural resource. So is a tree. Can someone go onto your land and start cutting timber for building material, just because it is a natural resource? Deer generally move from property to property. While they are on your land, they are, for all practical purposes, your property to do with what you please (within the limits of the game laws, etc.). Once they leave your property, you generally lose your claim to them, just like water flowing through your property (which is also often regulated as to what you can and cannot do with it).
That said, a deer spoiling in the woods because you didn't retrieve it is a sad waste that does no one any real good. Its a negative value change. To prevent this, I would retrieve the deer, talk to the landowner afterwards and offer him some meat if he seemed upset (or maybe even if he didn't) to compensate him for any sense of loss of privacy or for fewer rotting carcasses to feed the coyotes on his land, etc.