The whole point about your question is to define what is an "evolved trait"? The concept of "evolved trait" does not exist in evolutionary biology. Here are various definitions I can think of that could apply to the expression "evolved traits".
Does evolved traits mean heritable traits?
A trait may be heritable or not. See for example my answer to this post to understand what heritable mean. You may want to understand the difference between the narrow and broad sense of heritability. Greed is probably heritable as several studies showed that many personality traits are heritable. This post will maybe give you more info.
--> Greed is probably a heritable trait
Traits that evolve
Does evolved traits mean traits that can evolve?
Any (existing) biological trait evolves. Not necessarily because they are selected for or against, neither even for genetic reasons, but traits change through times. Culture changes.
--> Yes, greediness can evolve
Traits that are adaptations
Does evolved traits mean traits that are adaptations?
The concept of adaptation is not always easy to define and its definition may vary from authors to authors. Simply speaking, an adaptation might be defined as a trait that is now fixed in the population (meaning that all individuals in the population carry this trait) but when it was not fixed yet it was beneficial. Such definitions would not fit the concept of greediness if we assume there is some genetic variance for greediness. But while I am not aware of any study on the subject, a level of greediness very probably influence the fitness (=~ reproductive success) of its carrier. If someone is extremely greedy, he might not find a mate and may fail to reproduce. On the other side, someone that is extremely generous may give everything it has up to its life and would definitely fail to reproduce. Therefore, it seems at first though that there is what we call stabilizing selection on the level of greediness.
--> It depends on the meaning of adaptation. But yes, it seems intuitive that greediness is a trait that undergoes (stabilizing) selection.
Greediness is the kind of trait that are particularly interesting because it influences not only the fitness of its carrier but also the fitness of other individuals in the population. We say that it is a social trait and the field that study such traits is called social evolution. You'll need to get in touch with Hamilton's rule (Kin selection) and evolutionary game theory to understand more about the evolution of social traits. This post may eventually help you.