It’s generally best to pay what you owe, if indeed you do owe it. If you agree you’ve had the holiday pay but not the worked the associated hours, then I would pay it as it is honest and who knows you may need goodwill from someone involved in the future.
If you're not sure it’s owed I would get some advice, perhaps join a trade union, which is always value for this type of work and will not cost much.
As to whether Sainsbury would really go after it with legal action, I doubt it. But they may persist with letters, keep it on file or even sell it on to a debt collection agency.