Blood transfusions are generally recommended, when the hemoglobin drops below 7 grams, and usually, each unit of transfused blood (300ml) is expected to raise circulating hemoglobin level by about 1 g/dL.
The increase in hemoglobin level may only be temporary, and it could still take the body several weeks to regularly produce enough healthy red blood cells.
The results of treatment greatly depend on the cause of anemia.
It is well known that the number of blood units transfused is an independent predictor of worse clinical outcome.
Knowing the cause for anemia is most important!
Best wishes for your grandmother!