How to check that nothing is uploaded
You should not have to take our word for it. These checks work in any desktop browser and take about two minutes.
Watch the Network tab
Open the tool you want to check, then open your browser's developer tools: press F12, or Ctrl+Shift+I on Windows and Linux, or Cmd+Option+I on a Mac. Select the Network tab. Now choose an image and use the tool.
The list shows every request the page makes. You will see the page's own files and, the first time you remove a background or find faces, the model file being downloaded from this site. You will not see a request that sends your image anywhere. Select any request to see where it went and what it carried.
Use a tool with the internet turned off
Open a tool and use it once, so the page and any model it needs are loaded. Then turn off Wi-Fi or unplug the network cable and use the tool again with a different image. It still works, because the work happens on your device.
What the page is allowed to connect to
The site sends a Content Security Policy with every page, which tells the browser to refuse connections to any other website. You can see it in the Network tab: select the page request and look for Content-Security-Policy under Response Headers. It includes connect-src 'self', which means the page can only fetch files from image.redactninja.com.
What these checks do not cover
They show what this site does in your browser. They cannot tell you about browser extensions you have installed, which can read pages, or about software on your computer. If a photo is sensitive, use a browser profile without extra extensions.