That "maze" is called the Valve Body, and
the BB is a check valve or a plug depending
on where it was.
I would say if the trans isn't slipping, it just
needs the valve body gone thru, a sticking
valve body causes the problem you are having.
One other point, you got some courage to go
digging into an auto tranny and you don't know
what the valve body is called

Keep up the good attitude, you will learn lots,
I hope your next project works out like you want
Wild