The Not Today, Jeff! website and browser extensions do not collect, process or store any personal information.
The browser extensions contact the Not Today, Jeff! website when you visit an Amazon website in your browser, to check if today is a strike day. No personally identifiable information about users is stored.
The browser plugin needs permission to show the Strike! pop-up and countdown timer on Amazon domains. This requires permission to run code on those domains. The browser extension does not collect, interact with, process or store any of your personal information, or any data related to your visit to the Amazon website.
You shouldn't, and you don't have to. You can check out the source code for the browser extension on Github.