Looking in the "Index to Georgia Civil War Confederate Pension Files," by Virgil D. White there is not a Eliza J. Walters that filed for an Indigent Confederate Widow's Pension in the state of Georgia.

Remember that pensions were issued by the state and not the Federal government for Confederate Veterans and their Widows. If she moved to another state after his death, it is possible that she filed in her new home state.

I hope this helps.

Respectfully,

Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment