Your xh is about as dumb as they come. Here you just asked him if he remarried, then the credit card companies called the same day? So, what did you do? Did you go out on Twitter and tell the world? No...that's just how stupid he is right now.
Who knows, they may have called and she answered the phone. He may have changed his telephone number or put her on the account and she charged something. Stupid man....there are ways the credit card company could get the information.
I think the man doth protest too much. I think the man had an ulterior motive in contacting you today. I realize it's very difficult to let him go, but you have to. He's got to grow up and make his own mistakes in his own time and that includes that "ugly betty" woman he married.
I'm glad you didn't get into it w/him. The less you argue or defend yourself, the better for right now. He's still seeking justification for what he did. Step back, allow him to wallow in his mess.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.
