I accidentally burnt a nylon dish towel on the bottom of my best pan

You might try using a heat gun to heat the nylon enough to get it to peel off.. then keep working at it layer by layer till gone ... PATIENCE will be needed. move the heat gun around so as not to burn the pan and gently scrape the stuff off... clean well when done.

Warm the pan up with a hair dryer to try to soften up the nylon that is stuck. Use a razor blade to get it off, or even a nylon scraper. If any is left, try softening it up again and scraping it, or use a hot water soaked sponge.

Turn the pan upside down over a small burner on the stove. Have a piece of aluminum foil ready to collect the melted nylon. Use a metal spatula to scrape the bottom of the pan.

Nylon is not a great idea for a dishtowel. Not absorbent.

Thanks

Fill water up to where the problem area is and add a dryer sheet or two. Let it sit for a day or two and be amazed.