Non-owners deleting conversations from Outlook on iOS

Well everyone in the group has equal access, thus you do not need to be an owner in order to delete stuff. At least that was the initial intention, as at some point Microsoft seems to have changed the behavior. Looking at the mailbox folder permissions now, you can see that members of the Group get Author permissions, in other words they can only delete items they've created. You can easily confirm this by looking at the permissions, or by performing tests in OWA/Outlook.

# Get-MailboxFolderPermission default -GroupMailbox

FolderName           User                 AccessRights
----------           ----                 ------------
Top of Informatio... Default              {None}
Top of Informatio... Anonymous            {None}
Top of Informatio... Owner@local          {ReadItems, CreateItems, EditOwnedItems, DeleteOwnedItems, DeleteAllItems, ...
Top of Informatio... Member@local         {Author}

I imagine the tests you did via iOS were with the Author of the message, thus you were able to delete it.

On a side note, are your O365 Groups associated with your onmicrosoft.com domain, or a custom one?