Identity Based Encryption: Known Random Value
Thanks. I guess $K=g^s$. It seems trivial if Carol knows the random integer $r$ then she can learn the message. As you mentioned everybody could compute $T_{id}$ because both $Q_{id}$ and $K$ are public amongst the network. Since Carol knows $r$ then she can compute $Z=T_{id}^r$ and hash of this result!
To learn the message, she has to calculate,


  $$m=v \oplus H(Z)=m \oplus H(T_{id}^r) \oplus H(T_{id}^r)=m \oplus (H(T_{id}^r)\oplus H(T_{id}^r))=m \oplus 0=m$$


In general, Carol does not need to know the master secret key $s$ to read the message. The Encryption phase is randomized by the integer $r$ and for a Chosen Ciphertext Carol can learn the message. While we know she can not compromise the forward and backward secrecy of the scheme because the Discrete Logarithm is hard and the random integer for next ciphertext will be sampled, independently.