In its ordinary sense, ʿiṭr is perfume. But daqqū baynahum ʿiṭra Manshim functions as an idiom. One explanation relates it to perfume used in swearing a pact before battle; the textual tradition also offers other accounts. The poem need not be reduced to one asserted historical story.
The rhetorical effect matters more: an apparently pleasant word, “perfume,” becomes a marker of deadly conflict. This heightens the achievement of the mediators: they stopped not just resentment, but a cycle of lethal retaliation.