Asked girl out, she never got back, now she texts me a month later?

Met this girl a few months ago. Started chatting and getting to know her. One day after a nice conversation, I gathered up the courage to ask her to dinner and she said yes. Later that day I texted her to arrange a day, time and place. You would think that after the conversation went well and she said yes to dinner, she would be happy to pick a day. But instead of committing to a specific day, she gave the typical cowardly pathetic "I'll let you know". So I responded with No problem, let me know when you are free. Then I stopped all texts and calls to her. It has been a month. Neither of us has seen or contacted the other since my last message. Today, she texts me "Hi, how are you", as if the previous conversation never happened.

I'm not sure if I should bother responding. In my last text, I asked her to let me know when she is free. This does not look like her telling me she is free. I feel like I'm being gaslighted. If I ignore her, she will twist it around and accuse me of disrespecting her. But I don't want to be strung along all over again. Should I bother responding to her? What should I say? How do I show her that I don't want to talk to her again until she can commit to a date?

Updates
7 mo
1.
Before posting this question, I read opinions from several different sources:
*GAG posters, both Guys and Girls
*Professional dating coaches who are men
*Professional dating coaches who are women, advising other women to either commit to the date or reject, and not waste anyone's time with "I'll let you know"
*Girls on GAG who defend the horrible practice of telling someone "I'll let you know" with no intention of going on the date
Updates
7 mo
2.
Based on these sources, both men and women, the overwhelming consensus is that the best thing to do is send her a polite "Let me know when you are free", walk away and leave it completely up to her to get back.
Updates
7 mo
3.
As I am typing this, the responses to my question are divided between Guys and Girls. Zero Guys advised continuing to ask her out. But some Girls said to keep asking her and claimed that waiting a month with no followup from her was the same as expecting her to get back right away. And that asking what day was good for her was the same as expecting her to plan all the details of the date.
Updates
7 mo
4.
It makes one question the motives of Girls who advise Guys to continue chasing someone who treats them disrespectfully and most likely has no intention of going on a date with them. And Girls who disapprove of Guys walking away instead of continuing to be strung along.
Asked girl out, she never got back, now she texts me a month later?
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