If it's trademarked, and you don't own the trademark, then yes, it's illegal.

Unless, of course, the people who hired you to do the embroidery own the trademark and have given you express written consent to use it.

Go to the US Patent and Trademark site, get yourself comfy, and start reading under how to submit a design or idea in the FAC section and expand your reading from there.

Digitizing, as in scanning or copying, someone elses design or copyright symbol without the owner's permission is a definite no-no, hired by the owning trademark company to ditigize their design or trademark, that's okay. If you buy a manufactured card and the design and machine spits out a copyright symbol with the design, that's okay, it's part of the design and licensing agreement for the card, just don't sell the design on mass produced items without permission from the card manufacurer or owner of the image you are using.

I guess you could say the safe thing to do is get permission to use the image or copyright first or see an attorney specializing in intellectual property to answer any further questions. If you have developed a design or idea you would like patent, copyright, or develop a trademark for your own company, the intell prop attorney is the person to consult.