Compensating this woman for giving away a seat she bought and paid for is not "a good-will gesture," United. It's not even the least you should be doing. The stand-by passenger should have been removed since the seat already had been occupied. It was not available for you to give away again. What if that seat had been sold to a full-grown adult whose boarding pass "didn't scan correctly" and you gave it away to a stand-by? Would you have made that adult sit in someone else's lap?