At first I couldn't figure out what it was, but after thinking about it I had put line on a Steez SVTW1016SVSHL in that area. I had taken the spool out so I looked at the schematic for the reel and see that it is the spring.
I have never taken the reel apart beyond spool removal so I don't know how it came out or how to put it back in. If I remove the spool again will it be obvious?
Edit: After looking at the schematic more it appears that the way to get to this part is from the handle/star drag. I had backed the drag off to pull the old line off. Is it possible that is how it fell out?
Edit #2: I had also put line on a Steez 103HL and when I look at the schematic for that reel this part is called the Click Leaf Spring. Not sure why they changed the name over the years.
Edit #3: I found this video which shows how this is installed. https://www.youtube.com/watch?v=2FBwb6fCRj0. Problem solved.
And do it over a large cloth-covered area, so falling parts won't bounce.