Why did Tonks want to visit Dumbledore?

Question

In Harry Potter and the Half-Blood Prince, Harry is snooping around, trying to catch Malfoy. Once, he runs into Tonks on the seventh floor corridor, who says that she wants to visit Dumbledore.

Later at the end of the book, in the hospital wing:

And the meaning of Tonks’s Patronus and her mouse-colored hair, and the reason she had come running to find Dumbledore when she had heard a rumor someone had been attacked by Greyback, all suddenly became clear to Harry; it had not been Sirius that Tonks had fallen in love with after all.

Apparently Harry understands that Tonks had fallen in love with Lupin & why Tonks came to visit Dumbledore.

But I don't. What has Dumbledore got to do with Tonks & Lupin's relationship?

Why did Tonks visit Dumbledore?

Answer 1

Lupin has a special relationship with Greyback as you can read in chapter sixteen of HBP:

“You haven’t heard of him?” Lupin’s hands closed convulsively in his lap. “Fenrir Greyback is, perhaps, the most savage werewolf alive today. He regards it as his mission in life to bite and to contaminate as many people as possible; he wants to create enough werewolves to overcome the wizards. Voldemort has promised him prey in return for his services. Greyback specializes in children…Bite them young, he says, and raise them away from their parents, raise them to hate normal wizards. Voldemort has threatened to unleash him upon people’s sons and daughters; it is a threat that usually produces good results.” Lupin paused and then said, “It was Greyback who bit me.”

So he bit Lupin as a child to change him and recruit him for his army of werewolves. But it failed: Lupin now is a werewolf, but he did not join him. For Greyback he is a traitor. That's why it is likely for him to attack Lupin whenever they meet. Not to bite him again but to kill.

So when Tonks heard of somebody being attacked by Greyback she was immediately frightened it might have been Lupin. And therefore she needed information and advice from Dumbledore. Not because he could be "turned to werewolf" more, but because he could be fatally injured.