I have never seen someone poop a $50 bill or, actually, any bill.
What is this "we" as tourists business? "I" don't give money out to children (exception being a sweet given as change at a store) or anyone except close friends or for actual services rendered like a taxi, room cleaning etc. Before you pay a child for pictures perhaps it would be good to get the okay from their parents, don't you think? Yes, "you" and other's like you do share some of the blame and "no" it has not gone too far to stop. You can't be surprised that children chased you down as you were just giving out money, can you?
If you give a child the equivalent of 50 cents, do you really think it will be taken back to the family?
Perhaps it would have been better to take up a collection from the bus patrons and have Lenbert drop you by and give the money to Father Jim who would know how to get it to the people with the greatest need.
This only makes it harder for others to have a "no beggy-beggy" trip.
Just my personal opinion. No disrespect meant.
Peace and Guidance