I’ve never had a dial redone. The only time I can see this being a valid option is if a watch has sentimental value. Otherwise it’s always better to be patient and wait for an example with a better, original dial.
If this is a watch you already own and you’re looking at having the dial redone just make sure you see examples of their work before you proceed. Specifically, I’d want to see examples of similar dials to yours to ensure they have a good match for the font you need etc.
Finally, if you’re having the dial redone anyway, it may be worth first just having the lacquer removed and reapplied to see if the staining is on the top coat rather than embedded in the actual dial. Removing the lacquer will often take the dial print with it, but if you’re having it stripped anyway, this is a risk worth taking as you may be able to salvage the original print.