JSFiddle - React, Tailwind, and code Playground

JavaScript

var objTeste = [{
    "id": "03",
    "nome": "teste03",
    "pai": {
        "id": "02",
        "nome": "teste02",
        "pai": {
            "id": "01",
            "nome": "teste01"
        }
    }
}]

function recursiva(obj) {
    for (var k in obj) {
        if (typeof obj[k] == "object" && obj.hasOwnProperty(k)) recursiva(obj[k]);
        else if (k == 'id') delete obj.id;
    }
}
objTeste.forEach(recursiva);
console.log(objTeste);