The German Shepherd, named Irgo, arrived at a Wichita airport Thursday night after a flight on a private plane from Japan.
Kara Swindle and her two children were flying on United Airlines from Oregon to Kansas City, Missouri, earlier this week during a move to Wichita, Kansas.
When they went to pick up Irgo, they instead were given a Great Dane.
United said in a statement that the dogs were somehow put on the wrong flights during a connecting flight in Denver.
Swindle told "Good Morning America's" Michael Strahan Friday that she is considering a case against United Airlines. She did say she was pleased with United's efforts to return Irgo. She said the dog seemed healthy and happy to be home.
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The Associated Press contributed to this report.