You can look for your greatgrandparents on the 1900 and 1910 census. Those censuses ask how many children a woman has had, and how many living at the time the census was taken. The 1900 also asks for month and year of birth of everyone in the household.
You have year and state of her death, if you know full death date, and county where she died, you can obtain a copy of her death certificate, which should show the names of her parents. You might check with the library where she lived/died, see if the have old obituaries, or can tell you where to find back copies of the local newspaper. Survivors are often listed in obits. And, you never know what helpful little tidbits will show up in obits. Also, a good way to pick up married names of any daughters.
You give death date, but do not mention either how old she was, or when she was born.Even if you only have an approximate date of birth, that will put her in a time period.Over time records vary, and their availibilty varies, too. Happy Hunting.