This removes the title entirely to get rid of a duplicate sentence, resolving at the same time a <h2> problem... And offers a way to make the checkout choice of the date optionnal !

woocommerce_local_pickup_time_plugin_custom_2.php

<?php
/**
 * Remove the WooCommerce Local Pickup Time plugin checkout page select field title.
 * And offers a way to make the checkout choice of the date optionnal !
 *
 * @see https://github.com/WC-Local-Pickup/woocommerce-local-pickup-time/issues/103
 * @see https://github.com/WC-Local-Pickup/woocommerce-local-pickup-time/issues/104
 */
if ( class_exists( 'Local_Pickup_Time' ) ) {
    // Add a checkbox field to make the pickup date choice optionnal
    add_filter( 'woocommerce_general_settings', 'make_pickup_time_choice_mandatory', 20 );
    // Remove the default mandatory check on checkout.
    remove_action( 'woocommerce_checkout_process', array( Local_Pickup_Time::get_instance(), 'field_process') );
    // And add this custom one.
    add_action( 'woocommerce_checkout_process', 'my_not_mandatory_custom_field_process' );
    // Remove the default local pickup time field from the checkout page.
    remove_action( apply_filters( 'local_pickup_time_select_location', 'woocommerce_after_order_notes' ), array( Local_Pickup_Time::get_instance(), 'time_select') );
    // And add this custom one.
    add_action( apply_filters( 'local_pickup_time_select_location', 'woocommerce_after_order_notes' ), 'my_not_mandatory_custom_time_select' );
    // Hide the time select field if an other delivery method is choosen on checkout page
    add_action( 'wp_footer', 'hide_local_pickup_time_select' );

    /**
     * Add a checkbox field to make the pickup date choice optionnal
     *
     * @param array $settings General settings fields.
     */
    function make_pickup_time_choice_mandatory( $settings ){
        $updated_settings = array();
        
        foreach ( $settings as $setting ) {
            $updated_settings[] = $setting;
            
            if ( isset( $setting['id'] ) && 'local_pickup_days_ahead' === $setting['id'] ){
                $updated_settings[] = array(
                    'title' => 'Choix d\'une date obligatoire ?',
                    'desc'  => 'Si vous ne proposez que le retrait en magasin, vous devriez cocher cette case. Sinon, pensez bien à prévenir vos clients qui choisissent le retrait en boutique qu\'ils doivent penser à indiquer un créneau pour passer chercher leur commande.',
                    'id'    => 'local_pickup_pickup_date_mandatory',
                    'type'  => 'checkbox',
                );
            }
        }
        
        return $updated_settings;
    }

    /**
     * Process the checkout
     */
    function my_not_mandatory_custom_field_process() {
        global $woocommerce;

        // Check if mandatory
        $required = get_option( 'local_pickup_pickup_date_mandatory' );

        // Check if mandatory and set, if its mandatory and not set add an error.
        if ( 'yes' === $required && ! $_POST['local_pickup_time_select'] ) {
            wc_add_notice( __( 'Please select a pickup time.', 'woocommerce-local-pickup-time' ), 'error' );
        }
    }

    /**
     * Add the local pickup time field to the checkout page
     *
     * @param object $checkout The checkout object.
     */
    function my_not_mandatory_custom_time_select( $checkout ) {
        $required = get_option( 'local_pickup_pickup_date_mandatory' );
        echo '<div id="local-pickup-time-select">';

        $lpt = Local_Pickup_Time::get_instance();
        woocommerce_form_field(
            'local_pickup_time_select',
            array(
                'type'     => 'select',
                'class'    => array( 'local-pickup-time-select-field form-row-wide' ),
                'label'    => __( 'Pickup Time', 'woocommerce-local-pickup-time' ),
                'required' => ( 'yes' === $required ? true : false ),
                'options'  => method_exists( $lpt, 'build_pickup_time_options' ) ?  $lpt->build_pickup_time_options() : $lpt->get_pickup_time_options(),
            ),
            $checkout->get_value( 'local_pickup_time_select' )
        );

        echo '</div>';
    }

    /**
     * Hide the time select field if an other delivery method is choosen on checkout page
     *
     * @param object $checkout The checkout object.
     */
    function hide_local_pickup_time_select() {
        // Is the time select field required ?
        $required = 'yes' === get_option( 'local_pickup_pickup_date_mandatory' ) ? true : false;
        // If it's not required and we are on checkout page
        if ( is_checkout() && ! $required ) {
            ?>
            <style>
                /* Hide the menu by default */
                #local-pickup-time-select{display:none;}
            </style>
            <script type="text/javascript">
                // Wait for the page to be fully loaded
                // @see https://wordpress.stackexchange.com/questions/342148/woocommerce-documentation-list-of-js-events
                jQuery('body').on('updated_checkout',function(){
                    // Show the menu if the right delivery method is choosen
                    if(jQuery('#payment_method_cod').is(':checked')) jQuery('#local-pickup-time-select').show();
                    // Allow menu showing / hiding to take action depending of the delivery method choice
                    jQuery('#payment input[type=radio]').each(function(){
                        jQuery(this).change(function() {
                            // Show the menu if local pickup is selected
                            if ('cod' === jQuery(this).val()) jQuery('#local-pickup-time-select').show();
                            // Hide it if another method is choosen
                            else jQuery('#local-pickup-time-select').hide();
                        });
                    });
                });
            </script>
            <?php
        }
    }
}

Hello, which line of code is the one that is hiding the pop-up message "please choose the time for your pickup" that's showing (even when customer choose another method than pickup) ?

Thanks !