Forget about the EIP, which will be caught up when they file the 2020 return unless their AGI for this year will fully phase it out.

If the father was not a US citizen at the time the children were born and/or did not meet the residency requirements, then the kids were not US citizen at birth.  That's just my question about the children's ITIN and the identification of their correct citizenship.

My comments about SSN correction still stand.