The principle makes it an offence to use criminal force intentionally, knowing that it would cause or is likely to cause injury or annoyance to the person against whom the force is used. X, a well known social worker, pulled up a Muslim woman's veil in public without her consent, acting in good faith, and this caused her annoyance.
Since X used force on the woman without her consent in a manner he could foresee would cause her annoyance, the act fits the offence defined by the principle regardless of X's motives or his standing as a social worker.
Therefore, the correct answer is X has committed an offence by use of criminal force.
The fact that decides this question is what the principle actually asks for, intentional use of force known to be likely to cause injury or annoyance, with no carve out anywhere for good motives or public conduct. Testing each option against that narrow wording resolves the question.
Since none of motive, good faith, or publicness appear in the principle's own test, only the option built on the actual wording, intentional force likely to cause annoyance, survives.
Therefore, the correct answer is X has committed an offence by use of criminal force.