I'm sure the restrictions on what pets are allowed at Hogwarts came into place after the Marauders graduated.

When James or Peter forgot to do their homework Sirius would transform into his animagus form, climb on the desk, and eat their homework. They used the excuse, "The dog ate my homework," to their advantage.

When Sirius forgot their homework, James would transform into a deer and sprint into the classroom, eating his homework. The new excuse, "A deer ate my homework," was born.

When James and Sirius both forgot their homework, Peter would turn into a rat and eat their homework. "A rat ate my homework!" became another excuse.

After the animals ate their homework, Remus, the one who actually remembered to do his homework, sat at his desk, laughing. The other three Marauders carried smirks on their faces.