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.
let value: string = window.localStorage.getItem('treegridTreeGrid'); //"treegridTreeGrid" is component name + component id.
let model: Object = JSON.parse(model);//set the TreeGrid model.
window.localStorage.setItem('treegridTreeGrid', JSON.stringify(model)); //"treegridTreeGrid" is component name + component id.