Some tee shirt mfgs sew the tag in on its own row of stitches and you can just rip it out pretty cleanly. Most, however, sew it into the regular neck seam so if you rip it out it leaves a big ugly hole, or at least a damaged seam.
Once we had a local seamstress carefully remove the original tags and replace them with our own provided tags. I think it cost us about $1 each.
It's not awful to just cut them out really close to the stitches. Lots of tear-away tags that I've seen still leave this little white stub up in the seam after you tear the tag out. I remember thinking "i might as well have bought regular tagged shirts and snipped the tags out with scissors".
FYI you have to be really careful after you remove the tags because there are all kinds of guidelines and regulations on what has to be included on a garment tag (fiber content, manufactured country, garment care instructions,etc, etc) that you might get called out for at a trade show, so read up. Worst case scenario is BIG time fines.
Also, without tags it is really easy to get sizes mixed up so i would separate the sizes into different boxes for the whole process, whatever you do.
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