SS child benefit reduction paid baxk?

Any answer and sources on if I am 65, start my SS benefit now, start my minor child benefit as well - but I keep working, so my SS benefit reduced $0 due to earnings, as in my minor child's benefit. When I hit FRA at 67, i start getting paid back the money from my benefit reduction. Does the minor child benefit get the reduced money back as well or is it permanently gone?