Long ago, she abandoned her daughter at the local post office in a box that said free baby in one of her wild moments and then ran off with her apparent lover Lamar. She was apparently very irresponsible but despite this Granny continues to remember her fondly.
In the episode Holodeck Redneck, Granny uses the holodeck to live one of her two fantasies one of which is to be back in the arms of her Mammy prior to abandonment. The holographic Mammy was then beaten to death.