You can access Georgia Confederate Pension Applications at Ancestry.com through a Goggle search

georgia confederate pensions

His widow, Eliza Elliot Greene Schley died in 1883, 4 years after Georgia provided Confederate pensions. She is buried in the same cemetery as her husband. I would assume if she filed for a widow’s pension it would have been from the state of Georgia.

I have not been able to find an application under her name nor using alternate spellings. Nor could I find any for Capt. John Fannin Burch's ancestors.