I would not mess with the other person's response or lack of response. Does she look at you when you greet her? Some people are not taught to greet or are thinking other thoughts and don't even see the greeter. My husband was an executive and very surprised when some secretary at his large organization quit and one of her complaints is that my husband (who had nothing to do with her, did not know her or anything) never said "hello" to her when he passed by. I think worrying too much about the other person and what they are thinking/doing in relation to us, why they smile/greet/do not, etc. can backfire and we can find we are too "obsessed" with the other person like this poor secretary who cared whether she was greeted by this "random stranger", my husband passing her desk each day. If it had been the other way around, would she have been fired for not greeting an executive?