Sure! Here’s the completed dialogue with the correct possessive adjectives or possessive pronouns:
ANNA: Becky! Where are my silver earrings? Have you seen them?
BECKY: No, I haven't. But they're not yours! I got them from Julie, one of her friends, remember?
ANNA: Julie? Yeah I know her quite well. They live in Blackpool Road with their parents, don't they? And they have two Siamese cats.
BECKY: Actually, the cats are not theirs. They belong to my cousin, Alexia, who visits them every now and then. And that big Labrador retriever that you can sometimes see is hers.
ANNA: Do you think your parents will ever let us have a pet?
BECKY: I wouldn't count on it. They'll say that the parrot was ours and we didn't take proper care of it. And Dad will probably remind us how many times his cage was not cleaned out and he had to do it himself.
ANNA: Yeah you're probably right.