As a quick fix for Chrome, I installed this Chrome Extension, and added the following custom JavaScript to Google Inbox:
$(function(){
$('ul.pa.Y').append('<li class="oin9Fc cN just-mail" role="menuitem"><img class="io navIconDone" src="//ssl.gstatic.com/bt/C3341AA7A1A076756462EE2E5CD71C11/ic_product_inbox_16dp_r2_2x.png" srcset="//ssl.gstatic.com/bt/C3341AA7A1A076756462EE2E5CD71C11/ic_product_inbox_16dp_r2_2x.png 2x" alt="" aria-hidden="true" jsan="7.io,7.navIconDone,8.src,0.srcset,0.alt,0.aria-hidden" jstcache="990"><span class="sM" ti ee" jsan="7.sM,t-lp4cLVwXzdE,0.title,t-UXknpQ1iPuE" jstcache="991">Just Mail</span></li>');
$('ul.pa.Y').children().first().addClass('inbox-button');
$('<style>.hidden { display:none; }</style>').appendTo('body');
$('.just-mail').on('click', function(){
$('div.scroll-list-item.top-level-item').each(function(index){
var item_id = $( this ).data('item-id');
var thread_type = item_id.split(':')[1].split('-')[1];
if(thread_type == 'a'){
$(this).addClass('hidden');
}
});
$( this ).addClass('hA').siblings('.hA').removeClass('hA');
});
$('.inbox-button').on('click', function(){
$('div.scroll-list-item.top-level-item').each(function(index){
var item_id = $( this ).data('item-id');
var thread_type = item_id.split(':')[1].split('-')[1];
if(thread_type == 'a'){
$(this).removeClass('hidden');
}
} );
$('.just-mail').removeClass('hA');
});
});
The JavaScript adds a "Just Mail" item to the side menu of Inbox, which can be selected to hide the reminders. To see the reminders again, select the "Inbox" menu item in the same menu.
If you use this solution, you will need to update the JavaScript every now and then to be compatible with the updates made by Google. The above code has already stopped working. The accepted solution is more future-proof.