I think you may have triggered some concern or misunderstanding. What do you mean by "pretend it's private"?
The claim that "Your data is never recorded" may even be legally fraudulent. I'm glad that you don't record the data, but OpenAI does - making the claim as written a lie.
I understand why you made these decisions, but the website should not contain borderline false advertising.
The only way to guarantee something is private is if it never leaves your computer.