Alright, I figured it out. That piece is called the saddle, and it's connected to the arm.
I can't find anywhere to buy just the saddle, but by searching "dji mavic pro left rear arm" on ebay I found an entire arm with an intact saddle for $30 with shipping.
It looks like you can also buy them from Cloud City Drones, but they're out of stock at the time of writing.
Will update when it comes in!
2017-07-18 edit: it came in! Confirmed that that piece is part of the arm. Replacement was pretty straightforward - just a bunch of screws and minimal soldering. Some parts of prying the case apart were tricky, but nothing harder than an iPhone screen repair.