My(25f) GF(30F) keeps texting her ex bf(23?M) and won’t cut him off, knowing that it hurts me

TLDR: My girlfriend’s ex-boyfriend keeps texting my girlfriend from time to time, and my girlfriend won’t cut him off but often replies to them or doesn’t necessarily tell him to stop, knowing that it bothers me a lot. I don’t know if I can allow myself to be mad at her because I might be overreacting. What action should I take?

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My gf and I are in a same-sex relationship, and her ex is a guy she dated right before she went out with me. We both agree that he wasn’t a decent guy–I won’t go into much detail but from what my gf said, she thinks he only wanted her for money and sex as he made her pay for meals and hotel for 99% of the times, and pressured her into sleeping with him almost every time they went out together.

They broke up, and very shortly after we started dating. About 2 months after we started to date, he contacted her out of the blue and started talking about casual stuff such as ‘How’s your life these days’, ‘I’m back in town’, ‘Do you want to grab a drink and catch up some time’, blah blah blah.

I wasn’t aware that they were talking until she told me sometime later; at that point, they were having a conversation for about 2 weeks. I saw every text exchange they had and said “Babe, you are replying to him way too friendly it almost looks like you’re still willing to give him a second chance. He clearly still wants you, either genuinely or just for money and sex; and you not disclosing to him that you’re seeing someone kind of allowing his behavior.”

My gf explained to me that now that her ex isn’t that important person in her life anymore, she doesn’t think he gets to know whether she’s seeing someone or not(She probably feels uneasy to disclose that she’s dating a girl now, which I get it.) She gave me a couple more reasons why she texted him over the last couple of weeks, and after a long discussion, we both agreed that if he ever contacts her again, she’d tell him straightforward that she’s now seeing someone and doesn’t want him to text her, block him completely and get over with it.

That was a couple of months ago. Fast forward to now–her ex did reach out to her a couple of days ago, and my girlfriend told me today that he texted her, and she left him on ‘unread’ for a couple of days now. I am now mad and irritated by the fact that my girlfriend can’t be harsh on him. Her ex texting her isn’t something she can control & something she should be responsible for, I get it, but the fact that she just keeps letting it happen just makes me feel so little, so underappreciated, and sad. I don’t want to fight her over this but I also don’t want to keep going through this. Please give me any advice on what I should do in this situation; I love her so much and I don’t want this to ruin us.