Should I let my girlfriend go have dinner with an ex?

My girlfriend made plans to go have dinner at a "nice" restaurant with an ex. At least I consider him an ex because prior to meeting me, she dated him for a few months and slept with him on more than one occasion. She told me the relationship didn't last because the feelings between the two weren't mutual. My girlfriend and I have been together for a while now and she has told me I'm the only guy she has ever loved and that she wants to be with me for as long as she can. She tells me that the only thing she is looking forward to about the dinner is eating free food. This bothers me as well because I feel that if two people have dinner together at a nice place and they guy pays, it will appear more like a date than anything else. When I tell her that the dinner plans bothers me, she gets pissy. She thinks I don't trust her, but I do. It's the ex that I don't trust. I don't see why she should go have dinner with this guy in the first place. What should I do?