If you don't want them to put labels back in, you're really throwing money away to just pay them to remove the labels (it could add 10 cents to $1 a shirt, depending on the company....often the same as they charge for putting labels in too).
I'd recommend a few option, depending on the brand you use.
1) Most can be razored out as suggested above. However, don't slice the actual label, slice the 5 or 6 threads between the label folds (the little tuft of label on many shirts is a little tacky in my opinion, even though some major high street retailers do it). Then sew the new label, or just the gap if you have none, and all is done. You could get a Uni student on a fashion course to do about 100 shirts an hour this way, easily (if you can't use a sewing machine). It will look 100% original with the right thread and a basically qualified seamstress.
2) Use a machine with an unpicking ability. Same Uni option as about. We do this...luckily I have a housemate who is a qualified dress maker. She can replace 150 labels an hour for a cup of coffee and cooking her dinner.
