To answer this question, you need some background info first.
There are three "systems" used for the sense of smell. The first is the olfactory system. This system allows us to recognize what a smell is. You can tell the difference between gardenias and grass because of your olfactory system. The second system is the trigeminal system. This system tells you whether an odor is irritating or pleasing. It gets its name from the trigeminal nerve--the nerve that gives feeling to your entire face. Your sense of smell is all tangled up with the trigeminal nerve, meaning that some odors are painful to smell and some are not. When you smell ammonia and it stings your nose, that is the trigeminal system at work. The third is the vomeronasal system. It's thought to be use for detecting pheromones. However, it isn't important to this explanation.
So. What is meant by a "pure" odorant? It means that it only smells. It doesn't create a reaction in the trigeminal system. It only activates the olfactory system. Those who have lost their sense of smell are still able to distinguish many smells because of the reaction by the trigeminal system. One study I've read tested 47 different smells for people who have lost function in their olfactory system. Out of those 47, 45 of them were identified by the people with no sense of smell. The two that were not identified (decanoic acid and vanillin) didn't stimulate the trigeminal system and are thus considered to be "pure" odorants. In other words, pure odorants are odors that only smell and don't feel like anything. There are very few "pure" odorants, and peanut butter is one of them.
So, when someone says Alzheimer's changes the ability to smell, they have to make sure they're only testing smell and not touch too. That's why they need to use a "pure" odorant. Otherwise, the Alzheimer's patient might still be able to identify the scent and the test would be useless.