Hi Pav,
Some manufacturers sew the label in together as the collar is sewn with a coverstitch and/or overlocked seam. This method saves them money and it's fast. Taking the label out is a pain as it is integrated into the garment. You can cut it out very close to the seam and make sure it's all covered with a new label.
The coverstitch used in making tshirts is a special stitch that produces two straight stitches on top and a zigzag between them on the back. To emulate a coverstitch, you'd have to sew the new label in with two straight stitches - it would look like a coverstitch on the outside of the garment. The problem is once the original stitches have been cut into it can easily unravel. You have to sew over the original stitches to strengthen them.There is also an underlying overlocked seam that you may cut into removing the old label that can also come apart. You can zigzag this back together. Not many people have a coverstitch machine and the stitches need to be the same width as the original sewing to look the same on the outside of the garment.
Some manufacturers (you see it more on higher end apparel) sew the label on separately after the collar is sewn (label is usually sewn in with a single straight stitch and sometimes seen as a "box" of straight stitches or 2 vertical or horizontal rows of stitches). This can be carefully removed without affecting the underlying coverstitch and/or seam. New labels can be sewn in with a home machine by a seamstress.
In some cases (if your new label is similar material/colour as the old label), depending on how wide the label is and how far down the printing is, you can cut the original label down to 1/4" and fold it into your new label. This is tricky(if not impossible) to do with a wide label - it works with narrower, longer labels as opposed to short, wide labels. The old label might fray when you cut it, so you can apply a little clear nail polish or fraystop along the ege. It's a little bit of work. This method is a bit tricky, but do-able.
It's too bad all manufacturers don't sew labels in separately - especially manufacturers making blanks that know there's a very high likelihood that the label will be removed. I really appreciate the thought that goes into garment construction, when say, a designer will have the label sewn in with just a few stitches, knowing the buyer will take the label out for sure (for example: a crocheted scarf) and some even use a different coloured thread to facilitate removal. Nice!
But as a manufacturer myself, I must admit, it's pretty easy just to sew it in as you assemble the garment - no extra work/expense required.
Yes, the annoying world of other people's labels
