Is it permissible to feed the poor in lieu of making up missed Ramadan fasts due to a legitimate Islamic excuse?

You must make up the days you missed in Ramadan (definition). Feeding the poor is not sufficient, based on what is authentically reported from Aisha (may Allah be pleased with her), who said: "That used to afflict us, and we were commanded to make up the fasts but not commanded to make up the prayers," referring to menstruation. You are also required to feed one mudd for each day to a poor person along with making up the fasts, if you delay making them up until the next Ramadan without a valid shar'i excuse.