Likely etched via a sand etching type process. Not removable.

If the door is good, you can either live with it, cover it with a film that will mute the contrasting design, or replace the glass.

Weather sand etched or chemically etched one can usually feel it. It must be two pains with the etching on the inside. Replacing the glass is a fairly easy DIY if you can get a replacement cut for you.

I have seen just the insert replaced might be an idea.

Yep, steel or smooth fiberglass door, change the insert.