Hermione would initially be shocked and a bit scared. After all, anything related to Greyback is not good. However, being the strong - willed witch she is, she would quickly start researching in the library, looking for any information about the mark burn. She might also try some basic diagnostic spells to figure out what exactly the mark is doing to her or if it's spreading some sort of dark magic. She would be cautious around others, not wanting to put them in danger if the mark has some contagious or harmful effect.
Hermione would react with a mix of fear, determination, and scientific curiosity. The fear would come from the fact that Greyback is a feared and dangerous werewolf. But her determination would kick in almost immediately. She would approach the situation like she does with any difficult problem. She would analyze the mark burn from all angles. She might even try to communicate with Greyback, through some magically - safe means, to understand why he marked her. This would be a very dangerous move, but Hermione is known for taking risks when it comes to knowledge and solving problems. Along the way, she would keep a record of her findings, in case something were to happen to her, so that others could continue her research.