Example of how you can alter the description used in the calendar tooltips to allow HTML tags

functions.php

<?php //Please do not include the opening php tag if you have one.

function tw_ee_enable_tags_in_calendar_tooltip( $description, $datetime_in_calendar ){

	$event = $datetime_in_calendar->event();

	if( $event instanceof EE_Event ){

		$description = $event->short_description( 55, NULL, TRUE );
		if ( empty( $description )) {
			$description = $event->description_filtered();
			// better more tag detection (stolen from WP core)
			if ( preg_match( '/<!--more(.*?)?-->/', $description, $matches ) ) {
				$description = explode( $matches[0], $description, 2 );
				$description = array_shift( $description );
       				$description = strip_tags( $description,'<em><p><br><strong>' );
			}
		}
		$description = do_shortcode( $description );
	}

	return $description;
}
add_filter('FHEE__EE_Datetime_In_Calendar__to_array_for_json__description', 'tw_ee_enable_tags_in_calendar_tooltip', 10, 2 );

Reference:
https://eventespresso.com/topic/html-in-calendar-tooltip/