remove from session laravel and vue

Hi, i'm not able to delete data from the session. There are some data in the session . Now i want to remove one by one based on index value sent form ajax request.

//method to store in session, with ajax request
    public function store(Request $request) {
       
         $request->session()->push('product',json_decode($request->product));
         return session('product');
        
    }
//method to get data from session
    public function getFromSession(Request $request){
        
        $product = $request->session()->get('product');

        return $product;
       
    }
//delete method
    public function deleteProduct(Request $request){
       // dd($request->id);
   $request->id is the index value which starts from zero sent from view when user click remove button using 
     ajax request
 }

Route for delete

Route::get('/delete','ProductController@deleteProduct');

in view

//part of code
//getting data from session and looping 
      <div class="card-body" v-for="(list,index) in cart">
                        <img :src="list.image" width="80">
                       index:{{index}} {{list.name}}
                      

                        <button @click="del(index)">X</button>
             </div>

//....
            remove(index){
                axios.get('/delete',{

                     params: {
                        id: index,
                    }

                }).then((response)=>{
                //this.cart123.push(product)

                });
            }

Just what to know how to delete product based on delete from session and remove from page as well. Any help would be greatly appreciated

data in session: on dd($products) }

array:3 [▼
  0 => {#225 ▼
    +"id": 3
    +"name": "Ms. Clarissa Olson Jr."
    +"description": "Totam eius qui ut impedit nobis excepturi. Enim consequatur inventore dolorem laboriosam sequi dolore harum quibusdam. Doloribus ad tenetur tenetur et ut."
    +"category_id": 6
    +"price": 111
    +"image": "http://loremflickr.com/400/300?random=75"
    +"created_at": "2019-07-16 10:12:27"
    +"updated_at": "2019-07-16 10:12:27"
    +"qty": 1
  }
  1 => {#226 ▼
    +"id": 6
    +"name": "Kaylin Emard"
    +"description": "Et aperiam omnis nam iure id non fugiat. Excepturi voluptatem ipsam magnam. Esse asperiores ducimus enim et."
    +"category_id": 8
    +"price": 14
    +"image": "http://loremflickr.com/400/300?random=17"
    +"created_at": "2019-07-16 10:12:27"
    +"updated_at": "2019-07-16 10:12:27"
    +"qty": 1
  }
  2 => {#227 ▼
    +"id": 5
    +"name": "Prof. Iliana Mohr"
    +"description": "Autem sequi esse laudantium ut ut explicabo enim. Corporis cupiditate dolorum et ratione sequi architecto. Vitae enim ex hic nihil."
    +"category_id": 2
    +"price": 207
    +"image": "http://loremflickr.com/400/300?random=99"
    +"created_at": "2019-07-16 10:12:27"
    +"updated_at": "2019-07-16 10:12:27"
    +"qty": 1
  }
]
            }