Tee,
The green coloring may be simply a large bloom of algae or phytoplankton. The chlorophyl in these organisms gives it the green coloring. The bacteria in your skippy filter will not control this. The filter might mechanically strain some of it out, but I don't think you want your filter to do this as it will eventually clog it up and the algae will just continue to grow. The bacteria converts ammonia to nitrites and the nitrites to nitrates and the algae will live on the nitrates. Plants will absorb the nitrates so a few potted plants may help as they would compete with the algae, to some extent, but maybe not enough to completely remove the green color from the water. There are many methods that people use to eliminate algae, and some of them are mythical. The best approach would be to determine "WHY" the algae is growing so prolifically and then remedy that. In my opinion, it is probably due to a high concentration of DOCs and nitrates combined with the pH level. If that be the case, then you need to find the source of those and remove, hinder or alter them.
I would perform a chemical test of your pond water. If you don't want the hassle or expense of buying the kits, you can have a lab do it for you. If you contact your local agricultural extension office, they can direct you to a laboratory where you can have your water tested at a reasonable cost (maybe $30 - $45). They will send you an extremely detailed report of your water's chemistry. I do this for my well water at my cabin and the test results include everything you ever wanted to know about your water and things you don't and things you never heard of. That might be a very good place to start.
Catfishnut