After the greenway family accepted their neighbor's invitation to dinner, mrs. greenway felt obligated to invite the neighbors to christmas dinner. mrs. greenway's sense of obligation most likely resulted from

Mrs. Greenway's sense of obligation most likely resulted from "reciprocity norm".

The norm of reciprocity requires that we reimburse in kind what another has improved the situation us. It can be comprehended as the desire that individuals will react positively to each other by returning advantages for benefits, and reacting with either lack of concern or antagonistic vibe to hurts. 

It's most likely choice a, it makes the most sense in my opinion.