إِذَا تَطَيَّبَ الْمُحْرِمُ فَعَلَيْهِ الْكَفَّارَةُ، فَإِنْ طَيَّبَ عُضْوًا كَامِلًا فَمَا زَادَ فَعَلَيْهِ دَمٌ
Translation: If a muhrim applies perfume, compensation is due; if he perfumes one entire body member or more, an animal offering is due.
An entire member is a threshold governing the compensation. Perfuming an entire hand, for instance, differs from applying perfume to only part of it. The clause concerns applying perfume, not merely smelling a fragrance in the air.
Dam here is a prescribed compensatory animal offering, not “blood” in its everyday lexical sense.