How to repair wood table damaged by nail polish remover?

Have you tried a heat gun ,wipe off if it melts, then sand lightly, not sure !!.

sand area down & resurface,paint,stain,seal to match rest of table or redo whole top.

You will probably have to sand and re-stain the top of the table. Here is a video on how to do it without sanding it down.

https://youtu.be/nslbSjKR2BE

You can try Old English for dark or light wood where furniture polish is sold, OR try a wax treatment to the top. Here is a tutorial I found for you on this, it looks easy! https://www.hometalk.com/diy/bedroom/furniture/refurbish-wood-furniture-without-sanding-or-stripping-40253059

I would do the same thing that Pat Rios recommends.