When I was keeping marine aquariums, I got it a few times, and I would remove what I could, and then stir the sand to bury the rest. I don't know if what I did with the sand was recommended or not, as my only source of information was my local fish store.
If it is just on that decoration, you could simply remove it, and scrub it.
We have to deal with outbreaks on on Lake Champlain. According to the Vermont Cyanobacteria Tracker:
"Cyanobacteria grow well in water that has high amounts of nutrients like phosphorous and nitrogen. Cyanobacteria can multiply quickly to form surface scums and dense populations known as blooms, especially during the warm days of late summer and early fall."
This makes me think that you might have excess nutrients, and that heat may play a part.
I'm sure that there are other forum members with more knowledge on this topic and they should be able to add more about treatment and biochemistry.