The permit is an item that will grant you access to some of the closed off neutral areas.
In the NES version it is obtained after you beat area 6, and it is used to enter area 14 and area 18.
The permit is received after you beat area 8 in the Game Boy version. You'll need it to enter area 9.
The key card is acquired after beating area 2 in Bionic Commando: Elite Forces. You'll need it to enter area 5.