For the record, The first MCU film to be distributed by Disney was The Avengers in 2012. Paramount handled the theatrical run and initial disc releases of:
Iron Man 2
Captain America: The First Avenger
Thor was one of the early Marvel titles that was originally distributed by Paramount. Disney acquired the rights later on down the line. But if your disc is old enough to have come from Paramount, perhaps that's why it's not showing in Movies Anywhere? Paramount is not a Movies Anywhere...