I’ve gotten bills that had been written on with an ink pen, Even a few crudely drawn mustaches on the Presidents picture. I kept the one with horns on Washington for awhile because it made me laugh.
I’ve wondered what the threshold is before they can’t be used?
The average Dollar bill wears out after 18 months anyway.
http://www.trackdollarbills.com/blog/tag/dollar-bill/
Unless I am mistaken, the government does not “spend” the money it prints.
But in the OP, the money isn’t randomly returned and arbitrarily deemed in need of replacement, but removed from circulation altogether. If I write an IOU and it gets all tattered, I have to spend time writing a new one. If it never comes back… fantastic!
That explanation actually makes some sense. As “BANK” in your example, I’d be annoyed if my demand notes got messed with. OTOH, I’d be elated if they never ever came back again. If I were such a bank, I’d soak my bills in copper sulphate or something, and spread the rumour that they burn green. 
Urban legend at best.
If you can give a cite for this, I’d be surprised.
What you saw were “jukebox” quarters.
The owner of the bar/restaurant painted some red nail polish on some quarters and used them for “seed” money for the jukebox when things were slow. He could pick them out when the box was enptied.
Well, at the time I saw these red quarters, jukeboxes played for a nickel.
~VOW
…or restaurants where people write their name, name of favorite sports team etc. on dollar bills and staple them on the wall.
Or five plays for a quarter.
Just when was it you saw those quarters?
I’m in the coin business and I see these all the time. Always on silverquarters from before 1965.
Arcades used to do this, too. I was a regular at several arcades, and I’d sometimes get “bonus” quarters, that is, I’d give the cashier $5 and get 25 quarters, instead of 20. The extra five quarters were painted red, and the paint WAS always red.
It was much more common to get bonus tokens when an arcade used tokens rather than quarters. Usually the deal was that if you bought over a certain amount of tokens at once, you’d get more tokens than if you bought them a dollar at a time. The more you bought, the better the deal.
What would be the point of this? If he needs to put an equivalent amount of money back in the till at the end of the day, wouldn’t it be easier to just write down how much he put in? (Making up the difference with any old quarters he happened to grab, rather than having to fish through the box for the red ones.)
Early Sixties, before 1963.
So when I read about the so-called Urban Legend that these quarters were to protest Kennedy being Catholic and about to run a Presidential campaign, it made sense. Kennedy’s Catholocism worried the conspiracy-seeking people more than his war injury inspired patriotism in others.
(There’s ALWAYS a conspiracy, don’t you know?)
~VOW
The quarters were given to the employees to use in the jukebox when it was not playing. Painting them red made sure they ended up in the jukebox and not just pocketed by the workers.