NEC3 TSC: what's the best way to deal with work carried out by the Contractor under a Task Order that wasn't instructed in the Task Order?

Had a Contractor carry out work under a Task Order that wasn’t instructed but they’ve attempted to claim for it.

Is the best thing to do to notify these items as Defects and be explicit that these events are not compensation events?

If the Contractor has done works not instructed then this will not be a compensation event. Given that a compensation event is the only way that they can claim anything over and above the Price that they tendered for then there is no way that they can get paid for these, although it does depend on the option. Under option A they could not get paid at all for these items. Under option C or E they could get paid for them, unless they are a disallowed cost (under disallowed cost definition).

As you rightly say, these additional works are a defect (something not in accordance with the Service Information) that you could even asked to be corrected i.e. be removed (at no extra cost to you) - although I suspect that in most cases that would be unnecessary.