I would take it back to Publix, ask for the manager, and then request that he provide you with a dollar bill that has not been defaced. Take your receipt. If everybody who gets one of these demands a substitute, stores will stop accepting them.
That money is government property. It has been defaced. That’s why they can’t use real money in movies.
They’ll just cram them into change machines, soda machines, etc. It doesn’t matter what they write, or what they believe or trust in...it only matters what you believe and trust in. This little ploy is not furthering their cause, it just shows how immature and stupid they are.