I received another document and finally somebody had clear handwriting. On her son's, my great grandfathers, marriage record has her name listed as Janie Greenwood.
Now with the wonderful help from all of you, I did some more searching and came across a passenger list that fits her timeline. It appears that her family arrived Aug 11 1874 on the Britannic. It has a Mary Greenwood listed as being 17.
Should I follow through with this lead? How do I know it is the correct direction?