allow user to select pages from dropdown in my plugin

Change your code to this

register_setting( 'rex_plug_options', 'rex_plug_options', 'rex_plug_settings_validate' );
add_settings_field('rex_plugbox_text_exit_pop_selected_pages', 'Select Pages', 'rex_plugbox_text_exit_pop_selected_pages', 'rex_plug_box', 'rex_plug_main_box');
//with selectbox you cannot select multiple pages. If you need that try checkbox

function rex_plugbox_text_exit_pop_selected_pages(){
    global $rex_plug_options;
    if(!isset($rex_plug_options["rex_plugbox_text_exit_pop_selected_pages"]))   {
        $rex_plug_options["rex_plugbox_text_exit_pop_selected_pages"] = "";
    }
?>
    <select id="rex_plugbox_text_exit_pop_selected_pages" name="rex_plug_options[rex_plugbox_text_exit_pop_selected_pages]">
    <?php
    if( $pages = get_pages() ){
        foreach( $pages as $page ){
            echo '<option value="' . $page->ID . '" ' . selected( $page->ID, $rex_plug_options["rex_plugbox_text_exit_pop_selected_pages"] ) . '>' . $page->post_title . '</option>';
        }
    }
    ?>
    </select>
<?php
}