Just reach in behind the sliding tray from underneath with your right hand while seated in the driver seat. With the tray nearly fully pulled forward but not locked into place, reach in and you will find two plastic tabs that serve as stops one on each side. Pull each tab down and pull the drawer toward you as you do each side to allow the tray to slide past them. You should do the driver side one first then the passenger side. Once you have pulled the tray past the stop tabs the tray will come completely out. There will be an electrical pigtail connector to disconnect for the lighter. And thats all it takes. Then when you are ready to put it back in, just align to the sliders and shove it all the way in. The spring is heat staked to the back of the tray.
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Above was taken from an old post on F-150 forum. I pulled mine out after pulling off the radio/climate control dash bezel I just slid it open and removed it as above post says and the spring was laying in there. I ground off the plastic nubs and drilled/riveted the spring back on - works like new.