From the Super Mario Wiki
Kitty is the family pet of Junior and his parents. Due to the fact that she has to live in a house with the out-of-control Junior, the cat appears to have suffered some degree of abuse, as evidenced by the bandages on her leg and forehead.
When Junior broke two vases, he scrambled to place Kitty on the broken pieces, tricking his parents into thinking that she was the one who broke it. As a result, the mother scolded Kitty.