You can use filters to change the output:
add_filter( 'generate_post_date_output', 'tu_date_remove_time_tooltip' );
function tu_date_remove_time_tooltip() {
$time_string = '<time class="entry-date published" datetime="%1$s" itemprop="datePublished">%2$s</time>';
if ( get_the_time( 'U' ) !== get_the_modified_time( 'U' ) ) {
$time_string .= '<time class="updated" datetime="%3$s" itemprop="dateModified">%4$s</time>';
}
$time_string = sprintf( $time_string,
esc_attr( get_the_date( 'c' ) ),
esc_html( get_the_date() ),
esc_attr( get_the_modified_date( 'c' ) ),
esc_html( get_the_modified_date() )
);
// If our date is enabled, show it
printf( '<span class="posted-on">%1$s</span>',
sprintf( '<a href="%1$s" rel="bookmark">%2$s</a>',
esc_url( get_permalink() ),
$time_string
)
);
}