Girl emotionally attached to her ex? Do it keep it moving?

So I’ve been dating this girl for over a month and things have been going very well. We have good chemistry and it’s steady. I let her know my intentions from the beginning and she was on board. It was to date while vetting her for marriage. But after our 5th date, she mentioned she’s still emotionally attached to her ex after I let her know that way I'm treating her is how I would treat my woman that I pursue and deserve it. She still sees her ex at work and the girl the ex moved on to works there as well.
The breakup happened like Three months ago. Keep in mind, I didn't know any of these details, and she never showed any red flags about her ex while dating. It was also her first boyfriend and one she was physical with. I guess my only hint was the lack of emotional reciprocation, but that could have been any reason. After reflecting on the conversation, I felt lead on if she's been feeling this way all this time we’ve been going out. I'm not the type of person to wait for someone because I believe that's a waste of time, but she's a dope girl and a rare one. Do I cut her off?
Girl emotionally attached to her ex? Do it keep it moving?
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