You may be thinking of the TV-movie, Bagi, the Monster of Mighty Nature (1984).
Bagi, the Monster of Mighty Nature (大自然の魔獣 バギ, Daishizen no Majū Bagi) is a Japanese anime film that premiered on the Nippon Television network on August 19, 1984. It was written by Osamu Tezuka as a critique of the Japanese government's approval of recombinant DNA research that year.
The woman, named Bagi, turns out to be a "cat-woman" – a cross between a human and a mountain lion. She recognizes Ryosuke as the boy who had rescued her and raised her as a kitten when he was 6 years old. As Bagi grew and people became suspicious of the precocious "cat", who was able to walk on her hind legs and even learned to write her own name and speak, she escaped and grew to adulthood on her own for the next 9 years.
Upon their reunion, Ryosuke and Bagi join forces to find out the truth of her origins. Ryosuke's own mother is found responsible for Bagi's creation — Bagi is a product of recombinant DNA research between human and mountain lion cells. They then follow Ryosuke's mother to South America to confront her about the reason for Bagi's existence, but find a far greater peril. The officials in charge of the laboratories there are creating a strain of rice that has the potential to destroy humanity. Ryosuke's mother sacrifices her life to have Bagi destroy the "Rice Ball" and Ryosuke mistakenly pins the blame on Bagi, vowing revenge.
Meanwhile, Bagi is quickly losing her human traits and becomes extremely feral, attacking any humans that come near. Ryosuke catches up to her and stabs her when she attacks, but then finds a hand-written note held in a locket around her neck. He reads his mother's last words, expressing remorse for being both a bad scientist and a bad mother, and Ryosuke realizes his mistake and is filled with regret. He returns to the site the next morning to find Bagi's body gone, a set of footprints leading off to the distant mountains, meaning that Bagi has survived the stabbing and run off. He prays for Bagi to live on in solitude, far away from mankind. In the final shot, the silhouette of Bagi is seen running for parts unknown.
The Wikipedia plot summary seems pretty close to your description, and the cat girl, Bagi, does have pink fur.