How can I go back a previous level in The Tiny Bang Story?

I missed 1 puzzle piece and accidentally went to the next level.

How can I go back to a previous level to collect that puzzle piece?

There is no way to go back a level, but it doesn't look like that matters.

I just replayed the first level and left 7 pieces behind just to see what happens. It doesn't look like missing puzzle pieces has any effect on the jigsaw puzzle you get between levels. The game will give you all the pieces anyway.

My completed puzzle between levels 1 and 2 looks exactly the same as the screenshot in this walkthrough, even though I should be missing some of the pieces.