Picked up some nasty money from the bank the other day https://youtube.com/shorts/1F0vIj4wOn0?feature=share
I worked for a New York based bank and those bills would have not been put back in circulation. They would have been considered "soiled" and would have been sent back to the Fed for destruction. Bank policies vary.
I have a box of those blue light rubber gloves that I started using for CRH - it is no joke that money is absolutely filthy. I would definitely look into getting lightweight protective gloves