It is the only one that FreeBMD came up with when I searched for Walter Pittock from 1878 to 1882 in All Districts for Kent. So there is a very good chance that this one is yours. It is late 1879 I know, but every chance of being yours.
If one of those that I gave you from the census earlier is the right one so to speak, then you will have his family. Sandwich comes under the registration district of Eastry. So, if you are happy that your grandfather was born in Kent in 1880 it may well be worth you splashing out and ordering this birth certificate, which will give you fathers name, hopefully the mothers maiden name, plus the address where born.
If you do, please let me know how it turns out. Tom