he continued blithely

Lantern chose not to hear this. “However,” he continued blithely, “once we had taken a look at the somewhat dicky state of Brue Frères’s finances, and made a rough calculation of what old Karpov must have stashed away, we felt we understood you better: Ah, that’s what Tommy’s about! He’s hoping that old Karpov’s millions are going to see him very nicely into his old age. No wonder he doesn’t want anybody claiming them.

What does it mean by "he continued blithely" ?

Thank you.


Source: A Most Wanted Man by John Le Carre

"Blithely" means "without worry or concern". Whatever it was that he chose not to hear (what was it?) was probably something that should have worried him.