What item is a pushback operator holding up after pushback?
It's a steering bypass pin which isolates the nose wheel steering and enables the tug to turn the aircraft.

The operator holds it up so that the captain can see it to confirm that it has been removed.

This Wikipedia article refers to it

On some types, there may also be a "downlock" pin which prevents the nosewheel gear from retracting whilst the aircraft is on the ground.  In this case, the captain is looking for 2 pins being held up.  More often though, the ground lock pin(s) are removed before pushback and stowed onboard.