Oh, gosh, I’ve always wondered about this too! 
I’m honestly terrified Instagram might somehow know if someone tries to download something, even if it seems “anonymous.” Like, can Instagram track it back to you or could you get in trouble? And is it even safe to use those downloader sites? 
I’d really like to know if there’s actually a way to do this without anyone finding out—or if it’s just too risky! Maybe someone can explain how this works in super simple terms? 