Her past relationships did not work out. She is now currently married to you but & you are pursing a relationship i.e. have an emotional connection with an ex but claim it is friendship. It is understandable that your wife would feel insecure.
I suggest putting yourself in her shoes. How would you feel if she kept chatting to an ex, if there were an emotional connection to an ex, yet she claimed it didn't mean anything as it's *only* a friendship?
Let the ex fend for herself. You have a new 'obligation' now in that you chose a partner and she ought to be the one you are most concerned with. Not any exes.