Without that angelic expression, you could just suspect that the 24-year-old Pyrgos had been up to no good in somehow hastening their departures.
Two years ago, Pyrgos was at the back of the queue of Scottish No.9s, his path to the Test arena blocked by Mike Blair, Rory Lawson, Chris Cusiter and Greig Laidlaw. Since then, Blair has retired from the international game, Lawson has quit rugby altogether and Cusiter has battled against one injury after another. As a consequence, Pyrgos has scooped up nine Scotland caps over the past year, albeit most of them won as Laidlaw's understudy.
Still, that haul makes him not just a fully-fledged international, but a pretty experienced one at that. Cusiter, who played his first game in more than 11 months when he came on as a replacement for Glasgow against Exeter last weekend, has noticed a difference in his younger clubmate's bearing. "I've got a lot of time for Henry," said Cusiter. "The way he has developed is brilliant. His passing is better than ever and he has grown into an international player. You see him stepping up at meetings and at training."
That more assertive manner is in stark contrast to the shy and self-effacing figure cut by Pyrgos when he first signed on at Glasgow three years ago. He had just finished his degree course at Loughborough University and, although he had been tracked through the Scotland age-grade system by then, he admits now that he took time to adjust to his surroundings in a strange city and in a team of established big-name players.
"I'm quite a laid-back sort of guy," Pyrgos said. "When I came here, especially coming straight from university, it was my first senior opportunity. I wouldn't say it was daunting but it was a new thing to me and there were a lot of experienced internationals around me. As a young guy, speaking up is not always the easiest thing, but I've now been here for a few years and have played for Scotland so it's part of the job and I've got to be vocal. Every year I've got better and better and hopefully that will continue.
"I've been on the international stage a bit and I'm going into my fourth season here, so gradually I think I've become a bit more of a leader within the squad. Obviously, I'm a scrum-half as well, which is quite an influential position, so I've got to be vocal and get points across. I think I've definitely improved that area of my game."
The irony of his new status is that it might be easier for Pyrgos to get into the Scotland team right now than to nail down a starting berth at Glasgow. The arrival of the uniquely brilliant figure that is Niko Matawalu has been a game-changer for Glasgow - in every sense - and Pyrgos appreciates that the Fijian, who won a string of man of the match awards last season, has become the pulse of the side.
"He had a great season last year," said Pyrgos. "He's a really good player and a great guy and I get on with him really well. I just have to do as well as I can when I get the chances and put pressure on the coaches. It's tough. Obviously we, as individuals, have to put in good performances to merit selection. It's great competition with the two other guys and Ali [Price] as well. You want to be at a club like Glasgow, hopefully pushing for play-offs and to get in the final. Obviously it is tough at times but it is where you want to be."
Pyrgos started Glasgow's two most recent warm-up games - they played Harlequins before meeting Exeter - and is likely to be handed the No.9 jersey again tomorrow evening when the Warriors open their RaboDirect PRO12 season against Cardiff Blues at Scotstoun.
Cusiter, who looked reassuringly sharp against the Sandy Park side, is expected to be on the bench again. The pressure is constant.
Pyrgos said: "It's just the culture here. There's so much competition but you've got to be training well and playing well to stay in the team. There are Scotland chances as well when the autumn comes round, so you have to be pushing yourself all the time to improve yourself and to improve the club."
There is an impression at the moment that Welsh teams are struggling and haemorrhaging players, but it is not reinforced by the names that shine out from the Cardiff squad list. Yes, they have lost Jamie Roberts to Racing Metro, but the arrival of Gethin Jenkins from Toulon and Matthew Rees from Scarlets suggests, on balance, that they are actually stronger than they were a year ago.
"They've still got Lions players there, and Leigh Halfpenny was the man of the series in Australia," said Pyrgos. "They've got some really good young players as well. We've watched some tape of them and they play some pretty exciting rugby. It will be a really physical and tough game but we're excited.
"It will be great to start the season at Scotstoun. The crowd last season were brilliant. They really got behind us and it felt that the place really became our home. Hopefully we can kick on again and we can make it a fortress this year."