Among the children of William Sayle and Jane Greggor was Georgina and William.
Georgina married Thomas Cashen 1891 and Died 1902 which puts her out of the picture.

William married Eleanor Curphey and had a child Jane 1879, she is noted in census as Georgina- see Brian Lawson's BDM for all the details. It is this lady I think you are looking for.

Eleanor Greggor married Thomas Acheson 1865 and had your grandmother. Eleanor went on to marry Claudius Sayle and had James. I am guessing it is this James who is also in the photo and it looks like he married Fanny Whittaker in Liverpool West Derby R/O 1917.

There are a number of marriages for the name Jane Sayle in the index but not including Horne.
You may need to search the register after 1901.

Len Faragher