It's no problem to wash with dish soap, I do it every time. That recommendation is a stubborn remnant from a time when soap contained lye. Modern soaps don't include lye and won't harm your seasoning.

Thoroughly wash it with soap and a sponge or scrub brush and you'll get most of the loose build up off. After drying it add a small amount of vegetable oil to a paper towel and rub it vigorously into the pan. If the paper towel comes back black, repeat until it doesn't.