Maya was euthanised the same day she was caught, which was a violation of a state law that requires a five-day grace period.
Peta was fined US$500 ($685) for the violation, and had to pay more after Zarate took further action.
He claimed that the group operated under a policy of putting down healthy animals because it "considers pet ownership to be a form of involuntary bondage".
Peta denied this, claiming the 2014 incident was a "terrible accident".
The company settled the lawsuit, avoiding a trial in which Zarate's lawyers intended to ask the company about its past and present euthanasia policy.
Peta in the settlement agreed to pay the family US$49,000 and donate US$2000 to a local branch of the Society for the Prevention of Cruelty to Animals (SPCA) to honour Maya.
Zarate had originally sought up to US$7m.
The family's attorney, William H Shewmake, said: "The Zarates felt that the settlement reflects the grievous loss of their beloved Maya. And it allows the Zarates to bring some closure to a very painful chapter of their lives. They're glad the case has been settled."
Both parties said in a joint statement: "Peta again apologises and expresses its regrets to the Zarate family for the loss of their dog Maya. Mr Zarate acknowledges that this was an unfortunate mistake by Peta and the individuals involved, with no ill will toward the Zarate family."
This article was originally published by The Telegraph UK.