Why didn't the mutates jump Borden and Garnet at that back door?

Yeah, but Garnet said she had never seen the moon out in the open before, and there's no sign of fencing. Besides, they have such an aversion to outdoor living that they'd seem to have no reason to erect an open-air garden of some kind. Even when the crew goes out later on their mutate-hunt, there's no apparent worry that there may be a couple dozen beasts standing right outside waiting to rush in. You'd think they'd at least have TV surveillance (though this is strongly implied when the men first enter the main tunnel entrance -- and of course they monitor them in that anteroom before their first council meeting, and then Mories spies on them through that lamp thing).

But another thing -- though Garnet had never seen the moon out in the open before, she had seen it. This implies that the underground city had to have a glass roof somewhere, where people could see the skies or other vistas. But this too would seem inimical to their concept of security, since if they could see out the beasts could see in -- and have a conveniently fragile substance to keep whacking away at with rocks and stuff until it finally cracked and they got in that way. Maybe they only had exterior TV cameras through which to view the outside. But who volunteers to go out and install or repair them?

It seems the future city may not only have been wired but might have had its own version of the "glass ceiling". I noticed, no women on the council.

On the other hand, since Garnet had never been out in the moonlight before, Borden could at least take solace that she hadn't been out there playing post office with Mories at some point.