The 401/403/404 tension assemblies are a bit different from the 201/221/301. The thumb nut on the 201 merely screws on to the tension stud. On the 401 etc there are extra pieces. Who knows why the engineers changed the design. Boredom, maybe.
The 401 and 403 accept twin needles. Twin needles require two spools of thread feeding through the tension assembly and thus, into each needle. Hence, an additional disc is required for the added thread. I don't know if the 404 can take a twin needle. If not, Singer just used the same tension assembly as a cost effective measure. (Maybe?)
Start by locating the set screw inside the face plate on the machine. Loosen this. It is not necessary to remove it.
Once the set screw is loosened, the tension assembly should pull out. If it doesn't, try twisting it as you pull. It may be stuck with ages old dried oil.

