You don't need to stop drinking tea, it's just that it can inhibit absorption of iron. Best to take iron a few hours before/after drinking tea. Other things can affect absorption is: coffee, chocolate, calcium (dairy). Prob missed a few others, but you can look it up.
I too am thinking of ditching TRT as my blood thickens, but donating blood screws up my iron levels. My rT3 is already elevated, so I'm basically screwed either way.
But I'm ditching HCG (makes me feel really weird, and more depressed), as Nelson mentioned that it can increase HCT/RBC levels. Will also decrease TRT from 150mg to 100mg per week (split 50mg E3.5). Hopefully it'll stop the blood getting too thick in the future, who knows?
Good luck.
