Is carbohydrate an important part of phospholipid?
Your thinking is correct based on typical carbohydrates, but glycerol, the backbone of the phospholipid, is a 3-carbon carbohydrate that is usually derived from glucose.  It is not a sugar, but it does fall into the general class of polyols (aka sugar alcohols) that are a type of carbohydrate.

A carbohydrate definitely is an important structural part of the phospholipid, but your instructor probably should have been more clear in describing why that is the case; I can definitely understand your confusion here.