LS attacks, declares his DS objective. After the edge battle, DS attempts to play Backstabber to turn a 1-on-1 attack into a 1-on-2. However, Backstabber's reaction says to deal 1 damage to the engaged objective after this card enters play during an engagement... which it has just now done. And the engaged objective is his own... and it's 1 point away from being destroyed.
Has Backstabber just destroyed a DS objective? Or is the reaction designed to damage/destroy a LS objective at DS's discretion?