After using my dispenser for 6 months, I have noticed an added benefit; I use way less dish soap.
Empty hand soap container
PVC or CPVC purple primer (you could try a different paint remover, but this is what we had on hand)
In a well ventilated area, brush the CPVC primer on the painted parts of the plastic bottle that you want to remove. The paint comes off pretty fast, so be prepared to wipe off with paper towels.
I love my handy dispenser and the way it looks by my sink.
Note: A very faint ghost of the original paint outline is visible on the container when empty, which is why I would not make this project for a gift.