If you find them in your home, the best way to kill tick eggs is using table salt. Sprinkle a generous amount of salt over your carpet or couch cushions, and leave the salt for a week. The salt will dehydrate and kill tick eggs.
To kill tick eggs in the yard you can use commercially available pesticides. Mow your grass short to encourage ticks to leave. Since ticks can’t fly or jump, they depend on tall grass to bring them close to potential hosts.