Clean and Restain with Restore a Deck 4 years later

Hello I stained this fence almost 4 years ago and it still looks pretty good aside from the green mold. I called the sealer store and asked what to wash with before re staining. They said to use just dawn dish soap and water but that’s not happening on this 500ft fence. I need something I can apply with my pressure washer downstream or with a pump sprayer. My reservation on the dawn is it probably won’t kill mold on contact like bleach would. Sealer store rep said not to use any bleach product. I was curious if maybe tsp would be a solution. All and all I’d like to be able to apply whatever effectively and have it kill organics.