This patient had bone density performed on a Lunar machine the first time and on a Hologic machine the second time. There are differences in the way the machines read the bone densities. I am not sure how the 10% was obtained, but it was wrong.
To get a rough idea of change between scans using two machines, each bone density should be converted to the standardized units, and those can be compared. There will be at least an additional 3.5% error, but it is better than no information at all.
You can calculate the standardized BMD using the calculator on this web site, to see than she lost only 0.7%, which is not a significant loss.
The second mistake was doubling her dose of alendronate. The fracture rate is not improved by increasing the dose, and the bone formation may be over-suppressed.
You might have noticed that the Z-score decreased quite a bit, from -2.26 to -2.62, while the T-score was not very different (-3.60 to -3.66). These numbers cannot be used to compute the change in bone density because they were obtained using different reference groups.