How does the body repair extracellular damage caused by glucose?
The Wikipedia article on "Advanced Glycation Endproducts" (or AGE) is quite nice and in this case especially the section on "Clearance", which also contains a few references.
In short the AGE which are inside of cells are taken up by the lysosome and then broken down until AGE-amino acids are left. These are secreted into the blood stream and excreted with the urine. Bigger extracellular AGE which cannot pass through the cell membrane are taken up by special receptors first and then processed, here macrophages and Kupffer cells are included. An involvement of the liver is also discussed.

The following articles are also interesting:


Advanced glycation end-products: a review
The biology of the receptor for advanced glycation end products and
its ligands
Pathogenic effects of advanced glycosylation: biochemical, biologic,
and clinical implications for diabetes and aging.