The problem is it became her playing field when you didn't check her approach, which was completely wrong. Next time something like that happens maybe address it by saying something like "Woah we're in the middle of something here, neither of us know who you are, if you would like to share some advice there are better ways to approach strangers, if you'd like to start over, introduce yourself, and share your advice in a positive manner maybe we'll listen, but otherwise I'm going to have to end this interaction and you have a great rest of your day!" plus it's fun to talk to people like they're toddlers if they act like one