Greig agreed to terms on a four-year, $13 million contract extension with Ottawa on Friday.
Greig scored a goal on three shots, added two hits and went plus-2 in Thursday's 4-2 loss to the Stars.
Greig scored a goal in Sunday's 3-1 win over the Wild.
Greig scored a power-play goal on three shots, added three hits and went minus-2 in Saturday's 4-2 loss to the Jets.
Greig picked up two assists, one on the power play, in Thursday's 5-4 overtime loss to the Flyers.
Greig scored a goal on three shots and added two hits in Tuesday's 5-1 loss to the Sabres.
Greig (upper body) will be in action versus Utah on Tuesday, per NHL.com.
Greig (upper body) is a possibility for Tuesday's matchup against Utah, TSN 1200 Ottawa reports.
Greig (upper body) is expected to miss a week or two, according to Bruce Garrioch of Postmedia.
Greig (upper body) won't play versus the Kings, Claire Hanna of TSN reports.