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Osita obviously doesn't bear this mark. So other consciousnesses of Murmur he comes across won't be able to identify him as one of them except for the main consciousness. Which means he now has to stay clear of any body part of murmur he comes across or else he would be immediately killed. Not even out of spite but because it is something of shame to Murmur himself having something considered as a child of his own walking around without bearing his mark.

Most Cambion that can be considered successful in the abyss all bear a mark from their father or mother. The mark isn't something that simple to the demons, it represents a demon strength and deterrence level, so for Cambion not to be claimed means that the father or mother is weak and that means we can treat your property or name anyhow we want.