I'm going to lunch with a married woman
That's not good at all. Why didn't you tell your girlfriend?
I don't feel it is her business to know.
It looks bad to take out a married woman behind your gf's back. People might get the wrong picture of what you are doing.
You see, I really don't care what other people think of me.
But think of your girlfriend, you wouldn't care then finding out how she feels about you being with married women? If you're unhappy with your relationship, why not try couple counseling first?