Pietro:
A rabbit and a turtle. Pietro always compared you and his speed to a turtle and a rabbit.
Bruce:
A fish. Both of you are too busy to take care of a pet, so you guys decided a fish.
Tony:
A panda. Tony saw how much you liked a panda, and decide to adopt one.
Steve:
A dog(your favorite kind). Since Steve is old fashioned, he liked the idea of having a pet dog like people in the 40s.
Bucky:
A dog. Bucky saw this really cute dog when he helped Steve out to pick his, and decide de to bring to home.
Thor:
A pegaus. Being that it's Asgard, and you can't fly, Thor managed to find a pegaus and bring it to earth for you.
Clint:
An owl. Even though Clint's Hawkeye, you got him an owl because you like Harry Potter better than Hunger Games.