Regular Teams Personal group chats do not have an "owner" or administrator, so any member can add other users to this chat. However, if this group chat was migrated from Skype and in Skype this group was created as a "moderated group", then this feature is also transferred to Teams. This means that also in Teams, only the admins of this group can add new users.
If you were the only admin of this group, and now have left this group, then no one will be able to add you back to this group.
If you need access to the chat history of this group, then you should ask other members of this group do export the entire chat history of their account using the Teams export feature.
https://teams.live.com/dataexport
They can then extract the chat history of this group chat and provide it to you.