The aq_parent attribute of an object allows you to get at the parent. You can climb the object hierarchy looking for a greeting:
greeting = ''
while context is not None:
accessor = getattr(context, 'getGreetingText')
if accessor:
greeting = accessor()
if greeting:
break
context = context.aq_parent
This assumes you haven't changed the name of the Archetypes accessor for the field.