Can you identify this left over part?

That is the part that goes on the earphone, it contains the small grid. On most replacement screen it is already presinstalled so it probably fell of the screen you put in the trash. Still you could check if the screen you recently replaced has a protective grid on the earphone.

That looks like an earpiece speaker bracket from an iPhone 7/8/SE2 to me (same part on all). Often times a new screen will come with this piece pre-installed as @refurbish stated, but on at least the ones we use, the adhesive holding it in during shipping isn’t really all that strong and it can wander out of place. The screw that goes through that metal ring is typically what really holds it in place. If you still have those phones available, I would check and see if one of them is missing that bracket. If you don’t it shouldn’t be too big of a deal, I have tested phones without those before and it doesn’t really seem to harm anything major. Main thing it seems to do is help with noise isolation and prevention of dust entry.