Currently, when you tab through the fields in the template dialog, the info button and delete button attached to each field have their own place in the tab order (because we actively set positive tabindex values for them). So the tab order goes: text field, info, delete, text field, info, delete, textfield...
However, you can't actually interact with either the info button (e.g. by pressing enter to show) or the delete button (e.g. by pressing enter to delete) from the keyboard, so we should either change that or make it so tabbing moves directly between text fields.