In this case, you have a participle phrase which tells us about the owl. So you don't change tense. If you tried to make it past tense, you would have to rewrite the sentence, which would actually change the order of events.

euene6021, The verb "flutter" is in the infinitive form. This is a peculiarity of English involving the verbs of the senses. In the past tense we use see/hear/notice/watch + object + infinitive when we saw or heard the whole action. Using the infinitive means the action is complete. We don't need to use the past form of the verb. -I saw the man climb the tree. -None of them noticed a large, tawny owl flutter past the window. -I heard the car race down the street. If we witnessed the action in progress then we use see/hear/notice/watch + gerund. - I saw the man climbing the tree. -None of them noticed a large, tawny owl fluttering past. - I heard the car racing down the street.