Ex gf not right in the head?

After breaking up with my ex who works with me in different buildings, I cut contact with her and blocked her #. She's been emailing me once a month for half a year now. After a couple of months, I've told her I've moved on with someone and needed her to leave me alone. Apparently, she is also seeing someone as they've attended multiple company parties together.

My gf was upset and kindly contacted her to stop. She apologized to my gf, wished her well, and left it at that. I've given her a dirty mean look once just so that I could get it through to her head. The next day, she parks in my parking space. Then a month later, continues to email me. Her emails consist of messages as below.

"Random. I just got a dog, he's sweet. Feel free to meet him. I know how great quiet puppy time can be. We don't even have to talk."

"This store is having a Black Fri 15% off sale, thought I'd forward this to you just in case. Hope you and your family are doing well. "

"Remember this lil guy? *With attached pic of prank toy.* The receptionist found it under her desk."

What should I do? Should I continue to ignore her or should I confront her? It just seems like she doesn't understand when I do though. Is this her way of trying to keep herself in my life and interfere with my relationship? Is she trying to see if I still have feelings for her? I feel like I'm up against someone who isn't right in the head. Some advice would be helpful.

It can be difficult to understand what others are thinking, especially when they often don't know (with complete clarity) their own reasons for doing what they do.

A 90 degree perspective then...

I am assuming you broke up with her for reasons, and it's normal enough that those reasons can fade in intensity, but whatever those reasons, odds are at the time they made sense, and probably still do.

If you and your new GF are working out, and that is what you want, do whatever you can to put a stop to your EXes probing. Block, etc. Your new GF has already made it clear she is not comfortable with this. Perhaps later you and your EX can have some kind of friendship, but if your intuition is telling you she is playing games, trying to mess with your feelings, or just piddling in the pot to cause strife in your new relationship, trust your intuition.