How do I check that my logo really has a transparent background?

Short answer: Right after uploading it and before you save, switch the preview between “Light” and “Deep”: any leftover background becomes visible immediately.

Steps

On the “Shops” page, in the “My logos” tab, upload the logo — or open its details by clicking its thumbnail — without saving yet.
Under the preview, at “Based on the below previews, this logo is adapted for these textile colors”, switch between “Light” and “Deep”. The preview changes background color each time you switch.
Look at the edges of the logo:
- the logo stays clean on both backgrounds → the transparency is good;
- a rectangle or a halo appears on one of the two → there is background left.

The flaw almost always shows up on the deep background: a leftover white background is invisible on a light background and jumps straight out on a dark one. If you only run one test, run that one.

If a background appears

See My logo background did not become transparent.

You'll know it worked when: The logo stays clean on both backgrounds, with no rectangle or halo around it.