Do AI tools store conversations?

Hello everyone,

I am a PhD student and I am actually writing my research paper, I am using some AI tools like ChatGPT to check my writing and organize ideas, like when I write a paragraph, I copy paste it to ChatGPT to check if there are any mistakes or better formulation of phrases.

My concern is, does it store my paragraphs and results anywhere in the internet that can be flagged as plagiarism even if it's my own work?

Thank you so much!