Just looking over your puzzle, I would guess that the oval and
the two pieces at the bottom of the picture work together, maybe
to fit in the center of the puller. (just guessing)
The two pieces at the bottom have a ridge of metal about 1/2"
down from the top, and I see a dimple in them right there too.
I would guess that the two pieces go together, then slip the
oval around the two, the ridge holds the oval in place, then
tighten the bolt down into the dimple, and that holds them
together as a clamp for something.
.