Before I share my view based on my experience and knowledge, few points to remeber or reminder that is relevant to this situation.
Scrum is not a process it is tool.
Agile does not mean follow process, adopt the situation and it values more result rather than following process.
Scrum master is to serve the team in a way that team can focus on sprint and sprint related work only. Anything except the sprint work comnes in to the way of team, it is scrum master's job to isolate team as much as possible from that distraction/impediments or help team over come it with least disruption to the current sprint.
Now my stright feedback is YES, it is scrum master responsibility to remind team during scrum why they are doing scrum.
Here I see the few team members themselves are becoming impediments to overall teams progress. You could wait for retrospective and bring the discussion on the table as other members have suggested here but in you situation that mostky not end up good because the team is fairly new to agile. That approch works best for team who have been practicing agile for a while and not only understand most of the agile concepts but they have become self managed agile team. If you try this approch (i have done this ) mostly it ends up in blaming game and thats not we want to see in the team. I can explain why and how offline if you want to. For now i will move on to other aspect of my explanation.
Now lets focus on why and how?
Why scrum master need/should interrupt?
1)Because at this point scrum master is here to facilitate the quick communication and co-ordination between team members that help everyone to understand if team is making prigress on what tbey commited ? If not what is the blocking?
2)Because team members are fairly new to agile practice and scrum master needs to guide them what is the purpose of scrum. Its a quick update about work done and needs to be done for current sprint. Nothing more than that.
3)Because scrum master need to tackle any impediments that is blocking team making progress here clear communication is sure looks like impediment.
4)because scrum master needs to help team identify the waste and help them remove or overcome it. Over communication is waste here.
And many more I can relate but i guess you must have got my point.
How scrum master can handle this?
Specific to this situation I think reminding team members what they shod be talking about just right before the scrum is good start. Even by doing so if few mmebers are going way off consistently stop them right in scrum and follow up with their concerns. By thus time it should be pretty clear to scrum master that what is waste or intonational disruption and what is just lake of understanding. By doing so initially some members might feel tbey left out and not given enough info or update. But that ok. They will speak up in retrospective and mebtioned how they are feeling. Thats the time when scrum master can take their feedback and try to accomodate any valid inputs.
Bringing in original topic to retrospective is too late to remind and kind of recreating the issue and that why i do not think its effective for new team. For them this is hard to understand this is an actual issue or waste.
There are more ways we can handleand try it out.
Let us know if this make sense or if you feel positive about this approch. Happy to help offline or by any other way I can