I agree with
@addy1 - your pond will end up seriously overstocked with 40 koi. They are small now, but grow incredibly fast. And you probably added too many too soon... but that's water under the proverbial bridge.
I'm not much of a water tester myself, but whenever anyone gives water testing results they will say "everything was fine" or "all were within acceptable ranges". Posting actual values will give a much better picture. And it sounds like they tested before the fish were added to the pond - I'm not sure what they would be testing for with no fish in the system. Get a good test kit and learn how to do your own testing - in the early days of pond keeping it's really important that you know what's going on with your water.
Plants are an integral part of the pond filtration - you have five lilies, which is good, but they don't really do much for water quality in my opinion... unless you have them free-ranging in your pond, which I would not recommend. You need a LOT more plants than what you have. The plants will take up those excess nutrients in the pond and eventually starve out the algae. I use a planted wetland filter to filter my pond - plants and gravel (home to colonizing bacteria) keep my pond clean and my water healthy.
Every pond needs two kinds of filtration - mechanical, to remove the things that you can see (mostly broken down organics and other things that fall into the pond) and biological, to remove the things you cannot see. You are lacking the second. (Unless your waterfall is built on a biofalls or waterfall box filled with bioballs or other filtering media and you didn't mention it... ) You can sieve out organics all day long, but if there's no good bacteria to consume the fish waste and no plants to uptake the resulting nutrients, your system will fail. Now you do have bacteria in your pond - you can't avoid it. It colonizes anywhere there's a surface for it to cling to. But without a biological filtration system, your pond will struggle.
I know no one wants to hear that they have an overstocked pond, but it's a story we hear over and over again. Those tiny koi are so pretty and so... SMALL. But check out
@CometKeith 's thread about his goldfish (now with koi!) pond to see the growth you will get in just one year. And the amount of waste they produce is a big consideration when you keep koi.
Stick with us... you'll get to a clear pond and healthy fish with a few tweaks!