Rolliegla called it a vent, and that would seem to be what it is. The "valve" is probably a breather that is there to keep water from getting into the transmission.
Replacing the hose is definitely a good idea, but the hose itself is not going to be the solution to your problem.
The lack of a hose could allow transmission fluid to leak out, but the top of the housing looks clean, so that doesn't seem to be a problem.
If water (or something) has gotten into the transmission and contaminated the fluid it could be responsible for the TCC not locking-up properly.
If the codes return you should take it to a transmission specialist before you reset them so that they can better understand the cause.
Resetting the codes also erases the freeze-frame data that is needed for the diagnostics.
Sky NA 2007 Midnight Blue
Sky RL 2008 Carbon Flash - Naked