Hitomi's grandmother (Yuri Kanzaki in the Yuzuru Yashiro manga) is Mrs. Kanzaki's mother. She is unnamed in the anime. Her name is Yuri in the manga, but if Mrs. Kanzaki took her husband's last name, Hitomi's grandmother's last name would not also be Kanzaki.

When she was Hitomi's age, she was attending a summer festival when she was suddenly transported to Gaea in a pillar of light. There, she met Leon Schezar, who told her that he abandoned everything important to him to go adventuring, and when he saw her, wondered if it was in vain.

As he was dying, Leon wished, using the Draconian pendant he had found in Atlantis, to see her again. She returned, and Leon discovered that the power of Atlantis was the power of the heart. He gave her the pendant, and she returned to Earth. Some years later, she passed the pendant on to her granddaughter, and Hitomi held onto it as a good-luck charm.

She appears to Hitomi in visions, encouraging her to believe in her friends.

(Source: Escaflowne Wiki)