Pull the carb off the bike - in doing so, you'll need to take the top off and pull the slide/spring assembly out.
Look down into the top of the carb and you'll see the round chamber the slide sits in, and in behind it, a smaller, crescent shaped chamber. You can just about make it out in this drawing:
The plate you're referring to sits in that chamber, and is controlled by the choke lever/linkage (it's the bit on the drawing to the right of the slider that, usefully, isn't numbered). You may find that if you hold the carb upside down and shake it hard enough, the door and lever will fall out on their own, but if not, it's a case of working the peg on the lever out of the slot on the plate - you'll see what I mean. Refitting is pretty much the reverse of disassembly. It's not very complicated; it's just a bit fiddly.
Hopefully you can re-seat the spring because if the above fiche drawing is anything to go by, the plate isn't a part you can buy separately.
Hope that helps.