Wait, really? Why do they remove the tag? I actually like having the tag after purchasing something - it's kind of part of the package...
Every single H boutique I have been to and made purchases have done this. This includes Singapore, Malaysia, Italy, Paris (including FSH), Madison, Wall St, Riverside, and a sprinkling of others in Europe. The only time I had a price tag is when I asked for it back at the till (it was an orylag item, and I wanted to remember the name).
I think they might do it just in case the items are gifts, even from husbands to wives kind of gauche to leave the price tag on.