@Elanor posted this in another thread about getting the green boxes to disappear if you aren’t ready to collect them.
I’ve found if I leave my city and park on a slot for five minutes or so it seems to stimulate the HMP buildings to display a coin payment, which means the green boxes have gone back into CW storage. They only display again the next time I do a coin collection.
After the green boxes disappear, I can evolve monuments without triggering collection of any green boxes that may be on them.