Replace double backslashes before apostrophe in the email From Name and replace apostrophe html code with an apostrophe in the sitename email placeholder variable.

pmpro-fix-apostrophe-in-email-from-name-and-sitename.php

<?php
/**
 * Fix apostrophe's used in the from name and sitename email variable in emails.
 *
 * You can add this recipe to your site by creating a custom plugin
 * or using the Code Snippets plugin available for free in the WordPress repository.
 * Read this companion article for step-by-step directions on either method.
 * https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 */

function pmpro_email_sender_name_remove_double_backslashes( $from_name ) {
	return str_replace( '\\', '', $from_name );
}
add_filter( 'pmpro_email_sender_name', 'pmpro_email_sender_name_remove_double_backslashes' );

function pmpro_email_data_sitename_replace_apostrophe( $data ) {
	$data['sitename'] = str_replace( '&#039;', "'", $data['sitename'] );
	return $data;
}
add_filter( 'pmpro_email_data', 'pmpro_email_data_sitename_replace_apostrophe' );