Add a custom merge tag {custom_today_ymd}

gravityforms.php

<?php
// Create a custom merge tag for gravity forms.
add_filter( 'gform_custom_merge_tags', 'pj_add_custom_merge_tags', 10, 4 );
function pj_add_custom_merge_tags( $merge_tags, $form_id, $fields, $element_id ) {
	$merge_tags[] = array( 'label' => 'Today date(Y-M-D)', 'tag' => '{custom_today_ymd}' );
	return $merge_tags;
}

// Add a custom merge tag to the list of available merge tags in the form editor.
add_filter( 'gform_merge_tags', 'pj_add_custom_merge_tag', 10, 4 );
function pj_add_custom_merge_tag( $merge_tags, $form_id, $fields, $element_id ) {
	$merge_tags['today_date_ymd'] = '{custom_today_ymd}';
	return $merge_tags;
}

// Replace the custom merge tag with the value you want.
add_filter( 'gform_replace_merge_tags', 'pj_replace_custom_merge_tag', 10, 7 );
function pj_replace_custom_merge_tag( $text, $form, $entry, $url_encode, $esc_html, $nl2br, $format ) {
	$text = str_replace( '{custom_today_ymd}', wp_date( 'Y-m-d' ), $text );
	return $text;
}