• avadhyaḥ ayam — he is not to be killed
  Compound: a (not) + vadhya (to be killed). Verbal adjective fixing Bāṇa's status. The same word-family as ahiṁsā. Gauḍīyas note: Bhagavān's grace converts a verbal adjective into ontological protection — Bāṇa now belongs to the avadhya class.
• vairocani-sutaḥ — the son of Vairocani (Bali)
  Compound: vairocani (son of Virocana, i.e. Bali) + suta (son). Patronymic chain: Bāṇa son of Bali, Bali son of Virocana, Virocana son of Prahlāda. Gauḍīyas trace the lineage to anchor v. 45's Prahlāda reference: Bāṇa is in the protected line.
• prahrādāya varaḥ dattaḥ — the benediction given to Prahlāda
  Compound: prahrāda + dāyin (recipient) + vara (boon) + datta (given). Kṛṣṇa cites His own prior līlā as evidence; Bhagavān is the only one for whom past-life promises are present commitments. Gauḍīyas read this as proof of His tatastha-nityatva.
• tava anvayaḥ — Your lineage
  Compound: tava (your) + anvaya (line, descent). Kṛṣṇa addresses Śiva as the lineage-protector of Bāṇa. Gauḍīyas note: Śiva is given custody of an asura-bhakta lineage; this is consistent with his position as Kālabhairava and protector of asura-saints like Bāṇa.

• Bhanu Sw SB 10-63-47-53 - Lord%27s mercy upon demons and Supermacy of Krsna over Siva - ISKCON Chennai
  His Holiness Bhanu Swami· English

A king who once promised a saint that no descendant would be touched keeps that promise four generations later. Kṛṣṇa cites Prahlāda's vara, citing the contract of His own earlier līlā as Nṛsiṁha — Bhagavān is bound by no one except His own word, and that He honors absolutely.