Chosen Solution
I successfully changed both the battery and screen of my iPhone X. After putting together everything back, I noticed this part. Where does it go?
It’s one of the display clips. Probably from the old screen. It may have snapped off when you changed it. Or it was broken already if the display was damaged. The new display will have its own. And even if this was broken off the new display (which I doubt). It has many around the edge and if you replaced the adhesive liner as well, your screen should be in place quite soundly.
Hi, If the new screen assembly didn’t have it already, it looks like you may not have transferred it from the old display assembly to the new when you changed the screen.
(click on image) See Step.28 onwards in the ifixit iPhone X Screen Replacement guide
@jayeff, yeah, actually you can see the two clips at the top of the screen; I downloaded the large version of that image and they show up on that much better. Here they are, marked.
So yeah, that mystery part is definitely one of those two clips that broke off. You guys called it!