Hmmm, your question will probably become a more learning experience if you would make clear what Japanese word you want to know about. Given the English sentence, neither verbs make a natural Japanese sentence.
直す (not 直する) gets the intent of the English sentence but unnatural. But it is not so unnatural as the other choice. In contrast, 修正する is inappropriate. It sounds as if the teacher had to improve the questions or assignments in the homework.
If you are focusing on the English phrase "mark homework," then the ordinary choice of words are:
宿題を採点する or 宿題の丸付けをする