filter nested tree object without losing structure

You can create recursive function using filter() and also continue filtering children if value is Array.

var items = [{
  name: "a1",
  id: 1,
  children: [{
    name: "a2",
    id: 2,
    children: [{
      name: "a3",
      id: 3
    }, ]
  }]
}];

function filterData(data, id) {
  var r = data.filter(function(o) {
    Object.keys(o).forEach(function(e) {
      if (Array.isArray(o[e])) o[e] = filterData(o[e], id);
    })
    return o.id != id
  })
  return r;
}

console.log(filterData(items, 3))
console.log(filterData(items, 2))

Update: As Nina said if you know that children is property with array you don't need to loop keys you can directly target children property.

var items = [{
  name: "a1",
  id: 1,
  children: [{
    name: "a2",
    id: 2,
    children: [{
      name: "a3",
      id: 3
    }, ]
  }]
}];

function filterData(data, id) {
  var r = data.filter(function(o) {
    if (o.children) o.children = filterData(o.children, id);
    return o.id != id
  })
  return r;
}

console.log(JSON.stringify(filterData(items, 3), 0, 4))
console.log(JSON.stringify(filterData(items, 2), 0, 4))