What should a brother do who repented to Allah, but stole money from his grandfather without knowing the amount, and now cannot repay the sum or confess to his grandfather?

What your brother did is a betrayal and a sin. His duty is to repent, seek forgiveness, and return what he stole to its owners (your grandfather if he is alive, or his heirs if he is deceased). If he does not know the exact amount, then he should return what he strongly believes he took, and giving more is preferable. The debt remains his responsibility until he is able to pay it off.