Toilet seat repair / fix / croydex

And make sure that they are stainless-steel too. No point in putting in stuff which will rust in weeks.

It looks like there's two different methods for fixing this depending on whether you can access underneath the fixings or not. In your case you can so you don't need the rubber part at all, which is only needed for top fixing.

This explains it a bit better ...

It looks like you can use either fixing method if you do have access from underneath, either skip the rubber plug and tighten up the nut directly against the two washers underneath, or use the plug and, presumably, tighten it up really, really tightly, no need for the nut at all.

For a situation where you only have access from the top, the rubber plug is the only method.