The small hook tool is called a "spudger."
http://en.wikipedia.org/wiki/Spudger
You have to be very careful pulling the wires out, and using needle nose pliers or (ideally, a spudger) makes it easier to pull the wires straight up in the groove, reducing the chances of bending the insulation displacing blades. If you screw up the alignment of the blades, you risk a flaky connection (translates to potentially hours of gut-wrenching intermittent problems).
Also remember to use the "low" punch setting. Most modern panels and punch components do not handle the "high" punch power settings well... especially if your a "serial puncher " (three or four punches per connection ... bang, bang, bang, bang ... all on the same terminal).
FWIW