Perhaps if we badmouth Kabrinskia?
Yes.
Once they kill some Kabrinskians in battle it should decline again, right?
Good question actually. If Kabrinskians loot you, then yes for sure. If you win a battle in that region the flavor text ("The locals are grateful for defending their homes" or something like that) hints that sympathy towards you rise, but not necessarily that it is lowered towards the enemy. Is just fighting Kabrinskians generally sufficient? I'm not sure at all.
