This is the most expensive mistake in the category, and it is invisible at the point of purchase.
What firing does
Enamel ink is screen printed onto the mug, or applied as a decal, and the whole thing goes back through the kiln. At temperature the ink vitrifies — it becomes glass and fuses with the glass beneath it.
After that there is no layer to come off, because there is no layer. The mark is part of the surface. Commercial dishwashers, bleach and abrasive pads make no difference to it.
What the cheap method is
A low-temperature print or a lacquer applied on top of finished enamel. It cures rather than vitrifies, so it is a film sitting on a very smooth glass surface.
It photographs perfectly, survives a domestic sink, and degrades under repeated hot commercial cycles. In a cafe running mugs twice a day, expect it to look tired within a season and grey within a year.
How to tell them apart
Fingernail across the edge of the print. Fired is flush; applied has an edge.
You can also ask what temperature the decoration is cured at. A fired enamel print goes back to kiln temperature. Anything described in terms of drying or curing at low heat is not fired.
Designing for a fired print
There is a minimum stitchable line width in embroidery and a minimum printable one here. Hairline rules close up and very small type fills in. Open the artwork out rather than scaling it down.
Choose colours from fired references. Enamel colours shift in the kiln, so a screen match or a printed swatch will mislead you. We fire a sample and post it before the run, which is slower and is the only way to actually know.