In what ways does the injury inflicted by Bisclavarer upon his ex-wife reveal her true nature?

When the wolf sees her approach, he launches at her and tears off her nose!  Because he is able to prize loyalty over selfishness, and to accept his beastly side and address it maturely, Bisclavret ends up okay. On the other hand, his wife refuses to question her own selfish vanity and as a result suffers an injury that represents her inner ugliness. 

Thank you so very much once again.

No worries Greta.