What is the ruling on the prayer of one who discovers impurity on his garment while performing missed prayers for a legitimate reason? And must he repeat all the missed prayers, or only the prayer in which he discovered the impurity?

If you intentionally delay a prayer until its time has expired, this is one of the gravest sins. However, if the delay is due to an excuse such as sleep or forgetfulness, there is no sin in it, and it is obligatory to make up the prayer. If you realize there is impurity on your garment while you are praying, your prayer is invalid and must be repeated. As for previous prayers you performed with that impure garment, unaware of the impurity, they are valid according to the preponderant opinion.