I'd suggest having two buttons, "public scan" "private scan". That would contextualize the public scan to clarify and when you are scanning is publicly __listed__. And different colors. I think red for "public" would actually be the better choice.
Some information could be displayed while scanning. Idk put something like "did you know, using the public scan makes the link visible to others? This helps security researchers. You can delist it by clicking ____" or something like that and do the inverse. It should stand out. There's plenty of time while the scan happens.
> On each scan result page there is a "Report" button which will immediately de-list the scan result without any interaction from our side.
"Report" is not clear. That makes me think I want to report a problem. Also I think there is a problem with the color scheme. The pallet is nice but at least for myself, it all kinda blends in. Nothing pops. Which can be nice at times, but we want to draw the user to certain things, right? I actually didn't see the report button at first. I actually looked around, scrolled, and then even felt embarrassed when I did find it because it is in an "obvious" spot. One that I even looked at! (so extra embarrassing lol)
I think this is exactly one of those problems where when you build a tool everything seems obvious and taken care of. You clearly thought about these issues (far better than most!) but when we put things out into public, we need to see how they get used and where our assumptions miss the mark.
I do want to say thank you for making this. I am criticizing not to put you down or dismiss any of the work you've done. You've made a great tool that helps a lot of people. You should feel proud for that! I am criticizing because I want to help make the tool the best tool it can be. Of course these are my opinions. My suggestion would be to look at other opinions as well and see if there are common themes. Godelski isn't right, they're just one of many voices that you have to parse. Keep up the good work :)