I'm sure it goes without saying to anyone who has had the most cursory look, but don't just take a seam ripper to the shirt tags. Those stitches are integral to the structure of the shirt rather than exclusive to the tag. Removing those tags is a more delicate operation.
I have to say I don't remove IH branding without a twinge of guilt, and of course it can impact on potential resalability. For me it's partly that spending IH money on a shirt just isn't politic, socially or domestically, in my circles. I believe the gear, and the pleasure and fun of long-term ownership, is worth the coin, but I'm pretty keen to avoid that conversation with others. And I am concious of the irony implicit in the concept of high-end workwear.