Say someone is holding a number of items in front of you. What would you call the action you request that they perform to remove all choices but one so that you can examine the item that is left? It is important that the phrase let the other person know which item you want to be left standing.
Better, if it makes a difference, what is the action you perform on the object itself to get rid of its siblings?
For example, you say "Could you [blank] that item?" and they will remove the others.
Selection is the process by which something is chosen. Elimination is the process of removing possible options till one is left. If one wants X and does not want Y, one selects X and eliminates Y.
The other answers are good, but if I had to pick the best word to fit in your exact example I would choose "isolate."
"Could you isolate that item?"
Using "isolate" makes it clear that you only want that specific item and that you don't even want any of the other items near your selected item.
Of course this could mean that you would like to move the selected item to a different location instead of removing the surrounding items and leaving the selected item stationary, but I still think it gets the message across
Clearly, the word you want is select. You select one item from the group for examination; the other items are irrelevant.
select (v): to choose (as by fitness or excellence) from a number or group : pick out
I would call this paring down. When one pares down a selection to a single item, they remove all other extraneous items.
However, this may not be exactly what you want because it operates on the selection of items, rather than the one that is to remain.
Selecting one from a group is culling.
For your fill-in-the-blank question: "Could you retain that item?". It implies that the others should not be kept.
RULE OUT perhaps.
WINNOW OUT maybe.
ELIMINATE possibly.
I've often heard some politician is ruled out/winnowed out from candidates for presidency. The last one left becomes the president.
I've often heard some contestant is eliminated from a round of contest. The last one left becomes the winner.
EDIT: Could you keep or reserve that item? Which implicitly asks them to remove the other items for you. That still depends on your context, though.
In my opinion, the best option is single out. It is not too different from other options proposed in this thread, but to me it conveys better the idea of removing all items but the one requested.
If the intention is to examine the item you could say something like:
"Let's focus on this item"
