Summary section created on checkout-module. 
You can change **checkout_index_index.xml**, add item as '**quote**' & create js for  
***Magento_Checkout/js/view/summary/quote***

***Path - \vendor\magento\module-checkout\view\frontend\layout\checkout_index_index.xml***

    <item name="quote" xsi:type="array">
                                                                    <item name="component"  xsi:type="string">Magento_Checkout/js/view/summary/quote</item>
                                                                    <item name="config" xsi:type="array">
                                                                        <item name="title" xsi:type="string" translate="true">Quote</item>
                                                                    </item>
                                                                </item>
															
***\vendor\magento\module-checkout\view\frontend\web\js\view\summary***	

Also create **template** file in below path. 
  ***vendor\magento\module-checkout\view\frontend\web\template\summary***

You can override this file on you custom extension or update core files (Not recommended).
This might not be exact answer but might be workaround to you. 
Hope this help you.