In order for the PinIt button to pick full-size images they should be loaded and visible on the page. Since they are not, it cannot grab them to the grid gallery. As a workaround I would suggest to have a custom logic that pre-loads full-sized images before triggering the PinIt button click event. Something like this:
$('a[rel="lightbox"]').each(function(){
image_src = $(this).attr('href');
$('<img/>').attr('src',image_src).appendTo('#imageContainer');
;
})
$('#pinItButton').trigger('click');
This way you will pre-load all the images and put them into imageContainer block and then trigger a click that will open Grid Gallery to pick an image.
Hope it helps.