LOL, Sorry, I wondered about that and the only way I knew to make the Green Boxes disappear (not show) was to collect them! 
What @Elanor says make more sense for your answer. They “stop showing” when Buildings get more coins? So the faster your Buildings get coins, the faster they stop showing? 
I do think what I said about the Green Boxes not getting bigger after they appear is true. I looked at the NG post and only found this…
To me, this means they are still stored on the CW server (not growing larger) waiting for the next calculation of you City Collection and New Green Boxes. They will “Stack” on the Server until you collect them, But the Value of the Green Box already showing will never change.
Maybe @Night_Guy can chime in and let us know for sure?