Those who do not want to have bees but want the benefit of pollination pay someone to use their hives for that purpose. Payment can be bartered for a small operation.
Unless you are willing to rescreen the whole cage I would forget sieving out the unwanted.
I'm not into bees.
Intellectually, I am aware of their value to society as a whole and the hard time that anthropomorphic changes are giving them;
I appreciate them and their invaluable contribution to my existence.
But, I'm not 'into' them.
In part, my negativity may arise as a consequence of a couple of events in my life.
1) as a 9 y/o I was playing sword-fighting game with a few of my mates when we disturbed a wild bee nest and we got stung badly.
I spent 3 days in hospital in agony as a result. One of my mates, who it turned out was allergic, was there much longer.
2) As a teenager, I was in the back of a small van (Reliant Robin) making a journey to work one summer morning when a bee flew in a cracked window.
The driver, Richard, was one of those people with an irrational fear of all things stingy, and he panicked.
End result: A shallow bank at the side of the road; a huge amount of shattered fiberglass; and 3 months in hospital with a broken femure, collapsed lung; a hairline skull fracture and concussion.
Richard and the other guy, Tommy, both died.
I appreciate bees and their value; but my instinctive fear is not irrational.
I am thankful you came to a bee forum. I am hopeful you take the advice.
Would I have bothered coming and asking if I did not care about the answers or outcome?