The row comes as Ms Park was called for questioning and named as a suspect in the wide-ranging corruption scandal that eventually led to her downfall.
She was dismissed from her post last week when the constitutional court upheld her impeachment.
South Korea will hold its presidential election on 9 May.
Ms Park is the country's first democratically elected leader to be ousted.
Over the weekend Ms Park left the presidential palace, known as the Cheong Wa Dae, and moved into her house in an affluent district of Seoul.
Her nine Jindo dogs were not among the entourage that accompanied her.
The Busan Korea Alliance for the Prevention of Cruelty to Animals (Busan Kapca) noted she could have violated animal protection laws by leaving the dogs behind.
The group claimed she had abandoned her pets and offered to find new homes for the dogs.
A Cheong Wa Dae spokesman denied she had abandoned her dogs, and told Reuters that they were left at the palace partly because it would not be good for them to be uprooted from their home.
"She told... staff to take good care of the dogs and to find good foster homes for the puppies if necessary," said the spokesman.
Ms Park was known to be fond of her pets, which had been dubbed the country's "First Dogs," reportedKorea Times.
When Ms Park was inaugurated as president in 2013, she moved into Cheong Wa Dae with a pair of Jindo dogs which were given to her as a present.
The pair later produced several puppies, some of whom she kept while others were adopted. Jindo dogs are known for their loyalty and devotion.