While the king hadn't exactly invited her to approach and tend his wound, he hadn't stopped her either. The binding had been loose, so he lets her fuss with it.

"We will find no healers here, nor true safety."

Truthfully, if she had learned anything at all from her father, Arwen might be the closest thing they had to a healer here. Thranduil shifts his arm in his jacket so that it was comfortable, then checks to see that the hunting knife is still on his person. He had wiped it off, but traces of blood could still be found on it.

"I know your father, though it has been a long time since I have been west of the mountains."

He wasn't particularly fond of Elrond either, but he had to give him some respect.

"He would be grieved to know that you are here."