Peephole Removal – How to Remove a Peephole Viewer?

The "inside" handle (on the right in the last/lower picture) will have a small spring-loaded button on the handle post (the part you don't put your hand on when opening/closing). Use an awl or equivalent tool to depress the button and remove the inside handle. Then unscrew the inside trim ring (lefty/loosey) to expose the screws that hold the whole assembly together. Tighten em up and put er back together.

I'd suggest you chuck the door. Chipboard won't hold hinge screws well, nor will it make an attractive surface for the strike side.

If you were desperate to use this door, you could cut a channel in the chipboard edge and insert/glue a 2" piece of solid wood. Getting a really clean surface inside the channel would be hard.

At 31-1/4, you're pretty close to a 32" door, so you shouldn't have a hard time finding something appropriate.

For what it's worth, many in the door industry call this kind of door "solid core". I'd give volunteers at the Restore a little leeway for getting the description wrong.