Don't know what hole in BG's psyche that last post came from...
More relevant questions -
Are you poly?
Is she poly?
Is he poly?
(he, apparently, knows about you, and you know about him...good start!)
What kind of conversations have you had with you GF about what type of open-relationship model you are participating in? i.e. she had to call and ask if it was "okay" for her to go out to dinner with him. Is this an expectation of yours? Was she just confirming that this was within the confines of the relationship agreements that you have negotiated already?
"Going to Dinner" in my world doesn't require permission. "Going to Dinner" is not, necessarily a "date" in my rulebook - I go to dinner with LOTS of people for various reasons - not always romantic. It would be a good idea to sit down with you GF and discuss your expectations and assumptions are.