αυτοί τελείωσαν τη δουλειά
Verbs: Past 1, Lesson 4
One of the given translations of αυτοί τελείωσαν τη δουλειά is 'They've finished work' but I think it should be 'They finished work'. If I am correct, 'They've finished' is αυτοί έχουν τελειώσει
You ARE correct. But in British English the Present Perfect (have finished) is used instead of the Past Tense (finished) when you don't mention when the action took place.