Perhaps the easiest way to think about this is in terms of a sharp depreciation of the exchange rate. To the extent that this pushes up inflation (via “cost push” channels, and also via the stimulus to activity which a depreciation provides), how should an inflation targeting regime respond?
Of course the depreciation cannot be an excuse for allowing inflation to rise to a permanently higher rate. So, to the extent that the central bank’s objective is stated simply in terms of an inflation target, this clearly still has to be met. The issue is: “over what time horizon”?