Riley kept his face neutral. Chew started off well enough, but it was always best to keep things professional. Personal attacks or insults, even if delivered in a calm voice, will call into question a leader's objectivity and invite greater scrutiny as the higher ups review your actions.
As far as the Corporal was concerned, Chew's big mistake was putting the insubordinate Lt under the command of a green Sergeant. Riley personally disliked the tendency some people had of shipping their hard cases off. If you have a problem, fix it... don't pawn it off on somebody else. That being said, if she was a veteran Colour Sergeant or Warrant Officer, Riley could see it working. They'd have had to deal with hot shots and blow-hards for their entire careers, the Finn wouldn't pose any problem.
That, and as a Lieutenant equivalent at his age, Tarkka was probably an Other Rank that earned himself a commission the hard way. Or at least he'd been around long enough to respect other career soldiers that actually get their hands dirty. But he'd just got done insulting her a few breaths ago! Not only did Chew just insult the Finn, but he also put a junior Sergeant in a very tough position.
Yet again, Riley was forced to remain quiet. Having a Corporal come to his aid would do Chew's reputation no great favor, quite the opposite. Riley cursed the idiocy of having 3 officers in a fire team, two of which are bloody field grade! He remembered seeing a slide as Colonel Rock blew through their indoc briefing about XCOM rank conversion, and didnít' think it could happen fast enough. Of course, if we've got Colonels leading platoon sized 'companies' that'll still probably leave a Captain and a Lieutenant in command of our little 'squad'.
And of course, Tarkka wasn't cowed. Oh he said 'Sir' and eventually sat back down, but his words and tone were as bad as before. His threat had about as much subtlety as the flamethrower he carries, there's no way Chew can let him go on the mission now. The situation was far from over, but Chew needed to end it quickly. Riley still needed to bring up his own concerns about the plan and they were rapidly approaching their destination.