John Maine and Sean Green were probably already on the first flight out of town, but Carter is mildly surprising, as he wasn't yet arbitration eligible, meaning the Mets didn't even want him for ~$400,000.
Chris Carter hit .263/.317/.389 last season in 180 PA. His terrible footwork and noodle-arm made him a liability at any defensive position. Alderson probably (rightly) figured there were better dedicated pinch-hitters on the open market, should the Mets decided to go that direction with their bench.
Update: Adam Rubin adds a practical reason for parting with Carter:
I'm told there's a rational explanation for Carter. You have to make 60% of last year's salary, even in AAA. That's expensive if demoted.