DISCLAIMER: While writing this article, no lawyer or legislation was consulted. We do not guarantee the legality of the text presented here; we only aim to assist in your initial research. Before starting a clothing brand, you should always consult a lawyer.
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Here's an interesting question to ask and - even more so - to answer.
The answer is not simple (as becomes evident after a quick Google search) and, I must emphasize, it is specifically given for the promotional textiles we sell.
We work in the promotional space. Our printing activity involves buying a T-shirt from a white-label brand, printing it with your logo, and selling it to you. Many of our customers (and if you're here, it's because you have the same interest) also want to apply personalized tags and sell the T-shirts as if they were their own, as any other international clothing brand does.
Our interpretation is that this is legal. And we say this without any legal basis, but based on what common sense and experience tell us.
The articles we sell are not purchased from brand stores. They are made by clothing brands specifically for this purpose (printing, customization). So much so that nowadays several brands (such as Mukua, JHK, B&C, Sol's, etc.) make textiles without tags or with removable tags. Some brands even promote active tag swapping to use their own brand. It wouldn't make any sense for them to offer all these services and facilities and later raise issues because people take advantage of them.
Remember that we are talking about promotional textiles. We are not talking about going to a store like H&M, buying a piece of clothing, and putting on a new tag. That probably (and understandably) would be illegal. We are also not talking about counterfeiting (which is definitely illegal) by printing a registered logo.
We are talking about white-label clothing brands (TH Clothes, Sol's, Kariban, etc.) that are sold precisely for the purpose of customization and alteration. The context and manner in which this alteration or customization is done are extremely important, just as it is important to follow labeling rules and all legalities that fall on you as the owner of a small clothing brand.
Our opinion is that there will be absolutely no problem in altering a white-label item. There are other spaces and activities where this is done, such as in technology and promotional gifts. The promotional textile sector will not be different.
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UPDATE After an interview with Mukua, it was assured to us by their commercial representative that it is legal to change tags as long as we maintain all legally required information after the tag exchange.
You can find the complete interview here: Link to the interview (in portuguese)