If you grandmother is not having obvious bleeding, she may have bleeding higher up in the intestines. It may be occult (non visible) or appear as black, tarry stools. I would be concerned if she is taking any arthritis medicines, other than tylenol, as these can cause bleeding in the stomach. The elderly are at high risk for this problem.
The elderly are also prone to not eating well, and can suffer from iron deficiency anemia due to poor nutrition. Her doctor can order blood work and fecal tests for blood. There may be several possible causes for anemia, and a good work-up is in order to find the cause.
Here is some info: http://www.mayoclinic.com/health/iron-deficiency-anemia/DS00323
If her doctor cannot find a cause, and treatment is ineffective, request a referral to a hematologist (a blood specialist) or request a 2nd opinion.
I hope this helps and that she feels better soon, Paula