"He who marches out of step hears another drum." ~ Ken Kesey
Import it into Corel, covert to bitmap, select transparent background.Should do the trick unless I'm missing something.
Do they really need something more than this?Just cropped. Still a white background, but no square.
Ok, try this, but I have to tell you ahead of time, you will not be able to keep a transparent background in a .jpg format. I'm pretty sure the only way you can get it to keep its transparency is as a .png or .gif. Your DTG should be able to accept a .gif format.Anyway. In case you have any nodes in the image, draw around the entire image and GROUP. Convert to RGB Bitmap with transparent background. Edit in Photopaint, and use the magic wand to delete the white background. You may have to fiddle with the Tolerance to get rid of as much white as you can. Then EXPORT and Save as type ".gif". If you drop the .gif back onto your original canvas, you should see the background is transparent. Hope that works.
Don't use .gif or .png both those a serious compression formats. For DTG export as TIFF with transparent background, TIFF is lossless and retains all the details.