Two different conflicts wearing one costume
Almost every case like this contains a disagreement about the work and a damaged relationship, and they need opposite handling. Disagreement about the work — the shape of a service boundary, whether to write the migration now, how much test coverage is enough — is useful and should be resolved in the open with the whole team, on the merits, with a decision recorded so it stops being relitigated. Suppressing it is how teams end up with quiet resentment and no architecture.
The relationship damage is not a team topic. Interrupting, dismissing, reviewing code with contempt, going silent in planning: those are handled privately, individually, and directly. Putting them on a retrospective board in front of six colleagues converts a fixable problem into a public humiliation that both parties will then defend themselves from rather than address. An interviewer is listening specifically for whether you know which of the two you are looking at.
What you do first
Talk to each of them alone, and lead with what you observed rather than what you concluded. The difference is not politeness, it is that observations can be discussed and conclusions can only be denied.
"In the last three refinement sessions, when Sam proposed an approach you said 'that will never work' and moved on. Two people have since stopped putting forward options in that meeting. What is going on for you?"
Compare that with "you are being dismissive and it is damaging team morale", which invites an argument about whether they are a dismissive person. Ask each what they want to be different, and ask whether they are willing to sit down together. Do not carry messages between them; becoming the channel means the channel never closes.
Look for the cause outside the two of them
Sustained conflict between two competent adults usually has a structural feeder, and finding it is worth more than any amount of mediation. Common ones: two people who both believe they own the same component; a design decision one of them made that was reversed without explanation; unclear seniority where a nominal lead has responsibility but no mandate; a review process where one person is the sole gatekeeper for the other's work; or two people whose incentives differ because one is measured on delivery date and the other on defect rate.
Fix the structure and the heat often drops without anyone having to become a different person. Clarify ownership, set an explicit rule for how technical decisions are made and by whom, rotate the reviewer, or write the working agreement the team never wrote. Where the team is already routing around the pair, name that consequence to them, because most people do not know that their argument has become everybody's tax.
Where your authority ends
This is the boundary a weak answer misses. A Scrum Master or agile coach can facilitate, hold up a mirror, change process, and remove structural impediments. They cannot manage performance, issue a warning, or move somebody off a team, and pretending otherwise wastes weeks. So decide honestly which category you are in.
If it is friction between two people who are both acting in good faith, it is yours to work with. If one person's behaviour is a pattern that continues after a direct conversation, it is a line-management matter and you brief the manager with dates and specifics rather than impressions. If there is anything that looks like harassment, discrimination or bullying, it goes to HR immediately and you do not attempt to mediate it — mediation in that situation puts the affected person in a room with the source of the harm and exposes the organisation as well.
The other honest thing to say is that some pairings do not recover, and that a team where two people cannot work together is a team with a permanent capacity problem. Recommending that one of them move, with the manager who can act on it, is a legitimate outcome rather than a failure of coaching. What is not legitimate is letting it run for six months because addressing it is uncomfortable, while the other six people learn that this is what the organisation tolerates.
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