If you want to change the length of all excerpts, you can add this code to your child theme’s functions.php file:
function custom_excerpt_length( $length ) {
return 0;
}
add_filter( 'excerpt_length', 'custom_excerpt_length', 999 );
If you only want to make them disappear on your home page, use this CSS:
.home .excerpt-thumb + p {
display: none;
}