The real answer...
There is no simple answer for your question. The reason for this being that there is not a specific law that embodies all of the pollution issues that occur when a carrier is underway.
There are many laws, acts and regulations that the carriers must abide by.
The MARPOL is supposed to minimize water pollution. It specifically includes, oil, noxious substances carried in bulk, harmful substances carried in package form, sewage, garbage, and air pollution. The big problem with the MARCOlL is that when an incident occurs outside of a countries' jurisdiction when it becomes international waters, which is just a few miles away from land, then sometimes the jurisdiction can not be claimed, therefore making it easy for ships to abuse these rules.
There is the Clean Water Act, and it is trying to eliminate large amounts of toxic substances being dumped into the water.
This is an easy one to remember, it is called, The act to prevent Pollution from ships. With a name like that It sounds like it does more than it does, but it just regulates air pollution such as nitrogen, carbon and sulfuric dioxides.
With one carrier alone, it is estimated that hundreds and hundreds of thousands of gallons of sewage, gray water, which is caused by cleaning dishes, clothes, or bodies, hazardous waste, solid waste, such as the scraps you mentioned including the wood, and bilge water, which can be petroleum, oil leaks from the engine or machinery, do get into our oceans. This waste pollutes our ports, can spread harmful algae and other invasive species that can cause diseases such as caner and tumors, birth defects, can even be toxic animals, native marine life and contaminate our seafood.
The main problem with all of this is that it is very difficult to regulate and impose. We have to have some what of an honor system on these rules, and unfortunately, some people do not honor them.
So, I do think that the environmental activists do have a right to be concerned. It is a certainly has been an ongoing concern to myself.
Hope this helps!