Grieco played in every game as a tackle during his sophomore year at Holy Cross before converting to middle guard and becoming an All-New England performer for two seasons. . Her served as captain his senior year, when he was selected to the All East first team. He won the Davitt Award given by the Varsity Club as the outstanding lineman during his junior and senior years as well as the Connor Award given to the senior who was selected by his teammates as the one that they were most proud of. In addition, he won the Turco Trophy as the outstanding player in the Homecoming Game against Colgate in 1967.