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There are a few companies I have used in years past for redials and their work was O.K. but far from quality of the original for those in the know. I have been aware of a company that can make a dial just like an original but it may cost $1000 or so.
IMHO a re-finished dial is only acceptable under two conditions: 1/ the watch is very rare. 2/ The watch is very valuable. Yes, both of these would usually apply together. From a collector's perspective, a re-finished dial would reduce the value by at least 40% and unless it meets 1/ &/or 2/ above, I would pass. Otherwise the only value in a re-dial is either an unscrupulous seller trying to pass the watch off for something it isn't or someone trying to appeal to the Ooooh, shiny type of buyer. Patina is better than perfection in most instances.
Of course, there might be redials so good that they would be undetectable (even to the experts on this Forum). In which case we would never know, without forensic analysis of the ink, whether they even existed . . .
Highly unlikely at least for vintage omegas. I would say the collective knowledge here is enough to detect 99.99% of redials. And the .01% that is undetected will probably be for watches that are relatively common and not the rare/valuable ones.