The rescue kicked things off by saying they wanted to "set the record straight" after the dog made headlines following claims made by a former employee of Wilde and Sudeikis.
While Gordy was adopted by the now former couple when he was two months old, the rescue said "after giving him much love and training and travel adventures, [Wilde] realized that Gordy didn't love the travel life and wasn't happy around toddlers."
"Gordy had formed a very strong bond with his dog walker and in Gordy's best interest and after much thought and consideration, he was rehomed to his Brooklyn dog walker," MaeDay said.
The LA rescue, however, clarified that Wilde first consulted them before any move was made.
"We pride ourselves on finding that perfect forever home for our Maeday animals and every once in a while the animal is just happier in a different environment and that's okay," they said.
MaeDay also said they believe Wilde re-homed Gordy "out of compassion and love for him."
"We felt like we should share this because we hate that the media is painting a Maeday adopter in a bad light," the post concluded. "Thanks for adopting @oliviawilde and for being a responsible pet owner."
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The post from the LA-based rescue came on the heels of a media storm surrounding claims made by a former nanny for Wilde and Sudeikis -- one of which involved how the dog had been rehomed. There were also claims about how exactly the two split and that Sudeikis had been blindsided by Wilde's romance with Styles.
In response, the former couple released a joint statement: "As parents, it is incredibly upsetting to learn that a former nanny of our two young children would choose to make such false and scurrilous accusations about us publicly."
"Her now 18-month-long campaign of harassing us, as well as loved ones, close friends and colleagues, has reached its unfortunate apex," they concluded.
Wilde and Sudeikis share two children and were together for nine years.