The HO should be made aware of the fact that an aquatic habitat for water fowl is virtually impossible to practically maintain as a closed system. Water fowl are waddling poop machines. They may start with 4 geese, but the population is sure to increase with the breeding of the geese and the certain arrival of wild ducks. They would need to take out a mortgage to pay for the bio-conversion that would be required to keep it from becoming a cesspool and a health hazard and that is not even taking in consideration the cost of large enough pumps to create the flow rate that would be needed and the electric cost of running said pumps. If it could be continuously flushed (flow through system), then it could be make workable. Larger ponds, >1 acre and lakes can naturally sustain a resident water fowl population due to their size in surface area and capacity.
I know that you stated that they already have it dug, but better they find out now than later on when the smell will overwhelm them.
"Everybody is ignorant, only on different subjects." - Will Rogers