Reputation is the opinion that people in general have about someone or something, or how much respect or admiration someone or something receives, based on past behaviour or character. It is the good name/high regard that someone or something gets for good quality work or good quality workmanship. Of course it can also be used negatively for bad work and workmanship although the positive use is more common.
Repute refers to the opinion that people hold – in other words what other people think of you. It is when someone or something has a bad/good, etc. reputation. It is if you like more abstract in meaning and is used in expressions like: of high repute/of low repute – people have a high or low opinion of something.