Why does Gregg show up Felix in front of Dominic in Quantum of Solace?

Question

I'm having trouble understanding this double bluff between two characters in Quantum of Solace at around 36:30.

Dominic Greene : And I have a pest

Shows photo of James Bond to Gregg Beame

Gregg Beame : (to Felix) Have any idea who that is?

Felix Leiter : (to Dominic) Sorry.

Gregg : It's James Bond, British Secret Service. I don't know how I could have missed that.

Dominic : I will need you to get rid of him for me.

Gregg : Yeah. That's not going to be a problem.

Cut to airport arrival

Felix : You know who Greene is and you want to put us in bed with him?

Gregg : (Sarcastically) Yeah, you're right. We should just deal with nice people.

Gregg : I need to know you're on the team, Felix. I need to know you value your career.

I don't understand this exchange. Specifically:

1. Why does Gregg show up Felix in front of Dominic (which makes him look deceitful and therefore divided from Felix) if they are both in the CIA?
2. If not the CIA, what "team" is Gregg referring to and how does that have the potential to affect Felix's career?

It seems to me that this is a double-bluff. Gregg is trying to create a stronger allegiance to Dominic than to the CIA or his fellow spies. I just don't see the benefit in hanging Felix out to dry.

Answer 1

I think you are overthinking it. Dominic probably didn't realise that Felix actually knew who Bond was. There is nothing in the dialogue to indicate that. He wouldn't have picked up on the "I don't know how I could have missed that" being a jab at Felix, and taken it as just a genuine comment that Gregg realised he momentarily forgot who Bond was.

I don't think there is any other team here than the CIA itself. Gregg can see that Felix is having second thoughts about the operation, for ethical reasons, and doesn't want Felix's personal feelings to get in the way of the mission. I saw this operation as a kind of "CIA black ops" mission - covertly sanctioned by the US government (rather than something Gregg was doing entirely on his own). If Felix didn't play along, he'd show himself to be putting his own personal beliefs above those of his country, and that would surely be bad for his career.