"He was holding his hands in fists, threatening to beat us, but he didn't," the grandmother was reported as saying.
The woman said she was "very angry" at Mr Westwood's "awful" behaviour.
He was taken to the local police station but was not charged. Instead, he agreed to pay the girl's family 20,000 yuan (NZD$3900) in compensation and apologised.
A spokeswoman for the university said the incident had been caused by a misunderstanding and Mr Westwood's behaviour had not been acceptable.
His contract expired in August and would not be renewed.
Reports of the incident sparked anger online in China.
"He should go back to the country where he came from," was one comment quoted by China.org.cn.
"It is so ridiculous that such an ill-behaved man is even teaching students in university," another said.