"Didn't have to do" is more common than "needn't have done" in modern English. The topic came up in a recent discussion. https://www.italki.com/question/465160 Here are some comments by Su.Ki., a respected italki member. 'Need' is what we call a 'semi-modal'. This means that it sometimes works like a modal verb ( like 'must', 'can', 'may' 'will') and it sometimes works like a normal kind of verb ( like 'want'). Modal verbs form questions by inversion, negatives by simply adding 'not' or 'nt' and are followed by the bare infinitive. When 'need' is in its modal form, the question is 'Need I go?' and the negative is 'I needn't go'. Ordinary verbs form questions and negatives with 'do' in simple tenses and are followed by 'to' before the infinitive. When 'need' is in its (let's call it) 'ordinary verb' form, the question is 'Do I need to go?' and the negative is 'I don't need to go'. There is rarely any difference in meaning between the two forms. The modal form, 'needn't', is quite formal and old-fashioned. It is much more unusual than the more regular form, 'don't need to', and also much less useful. I wouldn't worry about trying to use 'needn't, if I were you.

"You needn't have" is almost obsolete. "You didn't need to" became more popular about 1920. Here is an N-gram. https://books.google.com/ngrams/graph?content=you+needn%27t+have%2Cyou+didn%27t+have+to&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cyou%20need%20not%20have%3B%2Cc0%3B.t1%3B%2Cyou%20did%20not%20have%20to%3B%2Cc0

Thank you, Angela! I hope that teachers only do it grammar coursebooks :)

Either one is fine. If I heard "needn't have brought" I would assume the person speaking was British; I wouldn't think they were _ungrammatical_. Also, teachers shouldn't yell at you for bringing an unnecessary textbook. That seems unwarranted.