I do have string aglae in the stream/waterfall where the fish can't reach it, but there is no string algae in the pond itself.
Water is still a bit green most of the time...
I responded in another thread but there's more info here so I have a different idea.
Unfortunately "green" can mean different things. Very hard to know without seeing the water in person.
Here's what I'm going to base my guess on...Normally a pond with string algae doesn't have what most people call green water. Caused by single cell algae. This green can be from bright, almost lime green to dark forest green. But in all cases it's like paint. You can only see down a few inches, certainly can't see the bottom. UV is what kills this type of algae. Normally what people will say after 5-7 days is something like "wow I went out to the pond today and could see the bottom". If you can already see the bottom then the UV's, or the string algae, have done their job. Actaully, because of the string algae you can probably turn off the UV maybe forever.
The next type of "green" is more of a tint. Couple of causes.
One case is being able to see the bottom but the owner will say the pond appears green. This can be as simple as macro algae growing on the bottom and sides giving the an overall appearance of green. In this case you'd be able see the shadows of fish being cast onto the bottom. The water is actually clear, just appears green. Chemicals have to be used to change this type of issue.
Another case, maybe most likely here, in that in older ponds (2,3,5 years) there can just be an accumulation of suspended particles. If you look close, like nose to the water, if you can see little suspended flecks like finely ground pepper, it would be a suspended particle problem. Algae grows in and on the particles and the particles can block the UV so the algae isn't killed. Also, single cell algae form clumps called colonies to protect themselves from UV but normally sun UV. UV filters normally kill the algae before colonies can be formed. Dead organic particles can also reflect green from the bottom and sides adding to the appearance of green water. But really the color of the water is more of grayish green as most of the lack of clarity is caused by already dead matter. Whatever the specifics if you can see suspended particles a fabric filter, like quilt batting, can be effective as the particles are very large compared to single cell algae. Bead filters can be effective. But best imo is a sand and gravel filter because not only will it solve the current issue it will do a good job of removing smaller particles than the bead filter and long term that's good.
Unfortunately the differences in the cause is very subtle but the fixes different. I used to clean ponds for a short time and it was pretty easy to tell just from the shade of green what was going on, but its impossible to explain. The best I've come up with is "can you see the bottom" and if yes, then "can you see the shadows of fish on a sunny day". Plus knowing the age of the pond. A UV filter is most effective in new bright green algae blooms.
My suggestion is consider the UV thing I said in the other thread and think about adding a sand and gravel filter. The quilt batting filter can be tricky and is really can of hit and miss. Water changes can so help, but it takes a lot of them.