Panel 1: Anthony states that he has no reason to distrust Liz and I believe him. He knows full well that Liz had no idea that Warren thought they still had a relationship.
Panel 2: He says as much and is gratified to hear Liz repeat what she said back to him as this is how people in Milborough confirm someone else's statement.
Panel 3: He then reminds her that he can't control who she talks to, sure in the knowledge that she won't talk to people that he might feel threatened by because they make her feel all squishy inside too.
Panels 4 and 5: He then says he wants to be sure about what and who she wants. This pleases her because she's got what she wants sitting next to her: a man who won't ask her to change who and what she is. Granted, what she is is a whiny, unadventurous mental pygmy with an ever-broadening arse but he does want her to be herself.