Solution

A recursive language is decided by a Turing machine that halts on every input.

If $\omega\in L$, then the machine halts and accepts $\omega$.

If $\omega\notin L$, then the machine halts and rejects $\omega$.

Rejecting means it halts without reaching an acceptable state.

Therefore, the correct condition is:

If $\omega\notin L$, then $M$ halts without reaching an acceptable state.