If the enablePersistence property is set to true, the treegrid property value is saved in the window.localStorage for reference. You can get/set the localStorage value by using the getItem/setItem method in the window.localStorage.
// get the TreeGrid model.
const value: string = window.localStorage.getItem('treegridTreeGrid') as string;
// "treegridTreeGrid" is component name + component id.
const model: object = JSON.parse(value); // set the TreeGrid model.
// "treegridTreeGrid" is component name + component id.
window.localStorage.setItem('treegridTreeGrid', JSON.stringify(model));