Does eating food touched by fire necessitate rinsing the mouth and washing the face and hands for prayer with the previous ablution?

Scholars have reached a consensus that ablution is not obligatory for that which has been touched by fire, after there was an old disagreement on the matter. It is not obligatory to wash the face or hands or rinse the mouth after eating something touched by fire; rather, rinsing the mouth is recommended for that which is greasy.