My boyfriend was submissive to his ex. It's annoying me to my core, should I just break up?

Anonymous
For some reason she went crazy last night and texted my boyfriend. Things like "Don't you ever forget you used to kiss my boots" and "I will own you for life".

The only reason I got to know this because I was using his phone at the time. He told me that she's crazy and anytime she does something like that he just deletes the text.
It means that it's not the first time she did something like this.

Should I break up? He didn't even block her yet and I don't want to tell him to block her, he's a grown up man.

I'm pretty sure he didn't bock her because he misses her. The reason I'm asking is because O don't want any stupid drama in my life. If it's a break up, it'll be straight up but he's a king of person who'll just use words and words and words just for sake of using them.
My boyfriend was submissive to his ex. It's annoying me to my core, should I just break up?
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