Just now he ____ his dinner but he says he will see you when he’s finished.

The phrase 'Just now' often implies a very recent past action or an immediate ongoing one. However, in this specific context with 'but he says...', it implies he has started or is eating. 'Has had' (Present Perfect) fits well for recent completion, but standard usage with 'just now' can be past simple. Given options, 'has had' is best for recent completion, though the context 'he will see you when finished' implies he might still be eating. Wait, 'has had' means he finished. If he will see you when finished, he is eating. Actually, 'has had' is the best grammatical fit for 'Just now' among options if we consider it means 'he has just taken his dinner'.