HT does reduce hemoglobin levels. This may be because women have slightly lower normal hemoglobin levels and it drops you to those, but that's a guess as no one has researched it. Pelvic radiotherapy also reduces your hemoglobin levels, probably because your pelvis contains a significant proportion of your bone marrow and it takes a hit. This usually recovers within a couple of months of the RT.
Looking at my data, my hemoglobin dropped as expected when starting hormone injections, and more during radiotherapy. I'm now almost 2 years after finishing HT and a year after getting my Testosterone back. My hemoglobin has recovered about half of what it dropped. Not had enough blood tests to tell if it's still improving, or if that will be it (next one will be February). So I do wonder if the treatments might result in a permanent drop.
Lack of iron or of Vitamin B12 can also cause anaemia, but hopefully they'll be testing those levels. I don't suggest you change any off-prescription supplements while they're investigating.
Also make sure they check your Testosterone level - if that's low, that might also hold your hemoglobin at female levels.