Work conflict, how should I deal with this?

Should I deal with it at all?

I work in an open office environment where no members of the public have access.

I admit to being a bit of a clown in the office and am liked by everyone who immediately works around me.

Around the corner, a woman works in a different department who is (from my observation) quite high strung. She stomps around and literally jumps by fright when others come near her at the kitchenette to grab a spoon or whatever.

I don’t really talk to her, barely see her and definitely have no work or non work related correspondence with her.

She recently had a falling out with the other woman in her team (team of two) who now has to sit in our department because things became so tense between them.

This morning, I was about to conduct a judicial conference over the phone when two people in our floor were discussing their weekends loudly. I asked if they could conduct their conversations in another area or more quietly due to my phone obligation. The woman who I have been referring to (we shall call Alana) suddenly said as she was walking past “Oh the nerve, like you are never loud~” in a really rude way in front of everyone. She continued walking back to her area as she said it – very passive agressive in my opinion.

Everyone is saying I should let it go but I personally feel a heightened sense of emotion. Anger and disbelief really. I want to confront her and tell her that I thought her comments were bullying and unprofessional. That if she has an issue with my office conduct, she should address it with me.

What would you do? What is the best course of action in your opinion?