Hi
Actually you can change the archor menu link from #id to http://yourdomain.com/#id or like this one http://yourdomain.com/specific-page#id
Then, when you click this link, the page will jump to that page and stay at the right position.
If you want to remove the menu link on a specific page, you need to view the source code of the page in your browser, find body tag like below
<body class="page page-id-2 page-template page-template-page-contact-php wpb-js-composer js-comp-ver-4.3.3 vc_responsive">
Record this class selector “page-id-2”
Then, find the HTML codes of the menu part, for exmaple, let’s remove this menu button
<li id="menu-item-304" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-304"><a href="http://demo.themevan.com/samsara/home-landing-page/">Home – Landing Page</a></li>
Record “id=menu-item-304”, now we remove it only on this page. Add the following custom CSS into Samsara options > custom styles > CSS codes
.page-id-2 #menu-item-304{display:none;}
Thanks