The shop owner accepts the bill and gives him $30 in change. At first, the different amounts can make the puzzle seem more complicated than it really is.
The stolen $100 returns to the register, but the thief leaves with $70 worth of merchandise and $30 in cash. Together, that equals a $100 loss.
So the correct answer is $100. The riddle is designed to confuse people into counting the stolen bill twice, even though the shop ultimately loses only the goods and the change.