I experienced the same problem with my C6510 paper tray extender and read all the help advice I could without being able to close the extender. No prodding, poking or forcing would close the tab.
FINALLY, here's how I did it. PULL the extender tab OUT as hard as you can while holding the tray with your other hand, you will almost "feel" it click, and while pulling outwards, move it left to its previously closed position. It works!
BTW, this tray can be removed from the printer and worked on separately which is what I did. It just fits in a grooved slot above the paper tray. While I had it out of the printer and working, I lightly sprayed silicone lubricant on both sides of the extender tab and worked the tab open and closed to lubricate, wiped it clean and reinserted the paper tray extender.