To answer to question directly, you can remove the first 'had' in your sentence. But I think there are other mistakes. What do you mean by 'noticed the way he would look hurt'?
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AnonymousShe had noticed the way he would look hurt when she had distanced herself away from him.
Do I need two 'had' here? If the sentence is standing alone, you don't need either of them.
"the way he would look hurt" = his habit of looking offended