Many people think eggshells "sharpen" disposal blades. In a dishwasher, they are a nightmare. The membrane inside the shell gets stringy and creates a net that traps other debris.
If the drain is stubborn, don't use a plumber's snake (it can puncture the thin plastic drain hose). Use air pressure. dishwasher pipe clogged
The clog is likely a waxy, fatty substance. The Solution: Melt it. Many people think eggshells "sharpen" disposal blades