Office etiquette for an extremely nosy co-worker?

We work in a relatively open work environment and sometimes this co-worker can hear both my personal and professional conversations that do not involve her. Later, she comments on them.

For example, when I recently called a store to confirm shipment on a coat I had ordered, she approached me three days later and said” so, I was hoping to see your new coat! you didn’t wear it today!” I had never even discussed it with her.

This has happened multiple times and I find it really offensive. I can close my office door for personal calls, but she still comments on my phone calls and conversations with other office staff. How do I tell her to stop it, without damaging a good working relationship?