Refresh can only be used with connections themselves (and those that represent data sources, such as a SQL table, an Excel file on dropbox, a SharePoint list, and so on), not with a function that is returned by a connection.
For your scenario, if you have, for example, a gallery whose Items property is bound to Office365_1.GetEmails({folderPath:"Inbox"}), then you can instead store the items (e-mails) in a collection, and bind the Items property of the gallery to that collection. On a button to refresh the items, you can retrieve the items to the collection again, and since the collection is bound to the Items property of the gallery, the (updated) e-mails will be displayed. You'd also need to initialize the collection once (possibly when reaching the screen where the e-mails are displayed). For this scenario, your formulas would look something like this:
RefreshButton.OnSelect: ClearCollect(emails, Office365_1.GetEmails({folderPath:"Inbox"}))
EmailGallery.Items: emails
BrowseScreen.OnVisible: Select(RefreshButton)
