Chatbots can retain a lot of information about your customers. Just think of the last time you looked at a product on a website and then saw an ad for it on social media. Just like cookies stores information, so do chatbots.
And customers want to know that their information is as safe as it can be.
It might be an added expense, but nowadays you really need to invest in security while creating your chatbot. After all, it has the potential to remember everything from what you sent your mom for her birthday, to your credit card information. Reassure your customers that you can be trusted.