Hi @martatracik ,
Understand and just like mentioned in your description, it's always been a difficult question to manage user's access to SharePoint list.
In you scenario, I think you can create a flow to send email to the "another team" you mentioned. You can use either "send email with option" action or the approval action:
Both of them are able to provide the response to flow and you can use update item action to do the update. However, for the connection of this update item action, you can use your own connection, which means the real update action will be done from your side instead of from the "another team", and they do not need to have access to the SP list.
Check connection of update item action:
Best Regards,
Heng Wang
