Note: this answer has been heavily edited, so some of the comments below might now seem out of place or irrelevant.
It seems that the meaning of "winnow out" varies: "winnow out" can be used to mean "remove what you want" or "remove what you don't want". It's real meaning may be closer to "separate", the verb.
I suppose it's a form of separation which is done gradually, by taking things out. You could throw those things away, and just keep what's left, or you could put the things you took out in a pile, and keep them.
Whether or not this interpretation is correct, it seems to mean one thing to some people and the opposite thing to others, including many dictionaries! eg the Collins dictionary lists examples using both versions:
http://collinsdictionary.com/dictionary/english/winnow-out
"The committee will need to winnow out the nonsense and produce more practical proposals if it is to achieve results." (remove) and "Time has winnowed out certain of the essays as superior." (keep).
A lot of people might just have no idea at all what it means - it's not a common phrase.
This means that using "winnow out" is liable to cause confusion, and so I'd recommend against it.
When we "screen out" something we're trying to remove that thing, like someone trying to detect a signal would attempt to "screen out background noise".
So, neither of them are appropriate in this context: "winnow out" is too informal (in my opinion) and potentially confusing, and "screen out" is wrong for the reason stated above: it suggests that the organisation doesn't want to see the best candidates.
I'd suggest "identifies" (if it just wants to find out who they are and not necessarily do anything yet) or "selects" if it wants to actually choose them.