The BGs for the girls' card are unlocked or by progression of their story or by stats, for example Taile Forge bg can be obtained after her event there.
Can you explain how to get them through stats, as it appears that the ones I'm missing are stats-based. I notice that the ones with BGs are either ones that allow for fun or ones that don't, so does it involve love or lust? Or is it a different? I haven't played the game for a while, so I'm kinda confused