You might want to discuss with your doctor the possibilities and other tests that could be run to find out what's causing the high ALP.
It has to do with bone loss caused by higher metabolism of those with hyperthyroidism. It's to do with how calcium, magnesium, phosphorous and vitamin D are metabolized and resorption and reformation of bone. Here's an article you might read to get a better understanding of it all:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3169869/
There's bone ALP and liver ALP... Bone ALP is, typically, higher in those with hyperthyroidism. High ALP is also seen with liver malfunction, hyperparathyroidism and other conditions.
If you google: "alkaline phosphatase with hyperthyroidism", you will come up with quite a bit of information.
Do you also have calcium, vitamin D and magnesium levels, along with PTH?