During the Hollywood writers strike a couple of years ago the writers for reality shows wanted the same pay as other writers. I assume that means that they do actually have scripts. Probably not all the dialogue is written out though.
Reality TV writers write “confessional” questions, in the case of challenge oriented shows (Survivor, Hell’s Kitchen, etc) write the challenges, and they do an initial pass on the stuff that got filmed to help construct the “plot”. So primarily they write structure, and pretty much no dialog you ever hear, which is why they don’t get paid as much.