When you book a hire car you kind of expect to be able to locate a pick-up point relatively easily. Niza Cars however, operate on a floating basis in La Linea, so your best bet is to head for the Tourist Office situated on the Spain/Gibraltar border. A company rep should eventually appear, but at least you have access to the Tourist Office whilst you wait.
Once you’ve been handed the car keys, and told where to deposit your vehicle, at the end of your hire period, you are free to hit the road (don’t forget you’ll probably now be driving on the other side!). Make sure you are clear about where to leave the car keys when you return your vehicle though, as you may find yourself wandering around the town aimlessly looking for a Niza rep.