Hi Annie! Thank you for posting your query on our Community

Only the “owner” of a conversation can remove a participant, like in a private conversation for example. In most cases, teammates will need to Unsubscribe from conversations themselves, notably for shared conversations.

Since these conversations, by definition, don’t have an “owner”, users can’t be Unsubscribed by other teammates or admins. 

One way that participants can be removed from a shared conversation is by moving that conversation to another inbox, that those users don’t have access to. When moving a conversation, anyone who does not have access to the destination inbox will be removed from the conversation. 

This can come in handy in cases where participants need to often be removed, and can even be automated to a certain extent, using the “Move to inbox” rule action, and the “Restrict participants” sub option.

I hope this helps!