If you are hearing a loud screeching sound
only during a cold and/or overnight startup, I found the fix.

It’s a weak battery. Replace your battery and it will fix the screeching sound during cold/overnight startup.

When you crank the ignition, the starter motor extends a gear mechanism that spins the flywheel. Once the engine is started, the starter motor will retract this gear mechanism. If the battery is weak, there is not enough power going to the starter to retract the gear mechanism fast enough, which causes the gear to grind with the flywheel and make the screeching sound.
This usually happens during cold, overnight starts. The screeching sound will go away if you drive around, stop, then start the car again because the battery has gained some charge from driving around.
This is a common issue on Honda Fits because our OEM type battery has low CCA or Cold Cranking Amps. Over time, the battery gets weak without warning and you will start hearing the screeching sound at startup.
I hope this helps anyone with this issue.

 

This is another reason why the original 151R battery (360 CCA) should be replaced with the larger 51R battery (500 CCA) when the time comes. Many people have done this.

 

I have the screech. Goes away if i rev the engine. Also noticed that the electric power steering seems not to be working at start up. The wheel will be stiff on start up but then gets better after warming up. I bet they’re connected. Will let you know after replacing battery.