The only thing incorrect about 2020 tax return is that the mother probably should not have claimed head of household.  Two unmarried parents can agree to let the lower income parent claim EIC and dependency which they did in 2020.  But I doubt her making 12K and him 70K allows her to claim she paid for the household.

As far as 2021 is concerned, she does not have to pay any back because she made less than 40K.  He is entitled to the full CTC amount as he did not receive anything early.