The children will not provide your client any tax benefits.
To qualify for either a Child Tax Credit, or Other Dependent Tax Credit, the child needs to be either a US citizen, a US national or a resident alien.
Your client's children do not meet any of those cases.
There is no reason for applying for ITINs for these children at this time as there is no tax reason for them to have ITINs at this time.
Publication 972 (see Qualifications for Child Tax Credit)
