Kathy - I don't know about mirf, but I can't find Jane in 1871. George was supposedly born 1871 near Wakefield. I was hoping his father would have been with the family ?
The only thing I can suggest is if you purchase a certificate for one of the children.
Have you seen this :
Birth, Jun qtr 1875
Joseph Edward Ward
Guisbro' Vol 9d, page 500
South Bank was in the parish of Eston which was in the Guisborough registration district.
Or better still, if you find the birth on TeesValley Indexes you could ask them to verify whether Jane was one of the parents before you purchase. We'd love to know the outcome if you decide to go ahead !
http://www.rootschat.com/links/0esp/ Best of luck !

Pels.