Greig played 41 total games in major junior hockey with the Medicine Hat Tigers and the Vancouver Nats in the WCHL in the 1971–72 and 1972-73 seasons, respectively.
Although he was a fairly skilled player, he was relegated to the role of an enforcer, primarily due to his weight and size, something which was coveted by professional teams during this era of the "Big Bad Bruins" and the "Broad Street Bullies".
On a conditioning stint, Greig then spent the remainder of the season (13 games) with the Seals' minor league team, the Salt Lake Golden Eagles.
However, in the '76-'77 season, interest was rekindled in the form of the World Hockey Association's Calgary Cowboys, who signed Greig for his fighting prowess.
Following two seasons saw Greig traded to the Cincinnati Stingers and Indianapolis Racers which had the likes of eventual superstar Wayne Gretzky and high scoring Blaine Stoughton on the roster.