Does riding during the Sa'i in Umrah due to foot pain make the Umrah unacceptable?

There is no harm in the one performing the sa'i riding due to an excuse. His sa'i and umrah are valid, and nothing is incumbent upon him. The Prophet (peace be upon him) circumambulated while riding due to an excuse, and he permitted Umm Salamah (may Allah be pleased with her) to do so due to her illness. The people of knowledge are of the opinion that walking is obligatory in sa'i and tawaf for one who has no excuse, but riding is permissible for an excuse, and no dam (sacrificial offering) is required then. Indeed, some jurists even consider riding permissible without an excuse, though walking is preferable.