Re-engraving is a word with a number of meanings in printing and as such context is required to discern the implied meaning.
See here of a listing of the meanings of "re-engraving" as used in printing and consistent with philately:
https://en.mimi.hu/philately/re-engraved.htmlEdit:
I re-painted today. Begs the information of what I repainted. Did I repaint the entire object (car, house, chair, sign or ...)? Did I just repaint a portion (where I could reach on the house, only the striped part of the car, only the blue color area of the chair, the hours on the sign or....). Did I just repaint a place where there is no paint because of a failure or alteration (the sanded new replacement car door, around the newly installed plaster around the replaced windows, the part of the chair which was too close to the fire, the sign back on the replaced broken front door window glass to the shop, or ....)
One word many meaning. Of course I did none of the above, I repainted toenails.
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Edit again. Even if done by hand on new steel, while a copy attempt, it is still a re-engraving in my opinion, which is an opinion consistent and covered within the meanings of the link provided. The third down seems to cover it and discusses American Bank Note re-engraving.
I think you are looking for a distinction in the term which offers yet more detail such as "copy re-engraving" or "re-engraved onto a new die" as two possible examples.
Another which after a while of thinking on the question is
Re(production)-engraving.