The couple had a quarrel, but they quickly made up.
Literal
That married-couple [topic-は] quarrel [object-を] did [but-が], immediately reconciliation [object-を] did.
けんかをした...仲直りをした — two suru-verb phrases linked by が ('but'). その夫婦 ('that couple') uses その to mark a specific, known couple. 仲直りをする ('to make up/reconcile') is the standard expression for patching things up after a fight.