Well, I found it:
function get_the_excerpt_filter( $excerpt ) {
$wordToRemove = "Introduction";
$len = strlen($wordToRemove);
if(substr($excerpt, 0, $len) == $wordToRemove){
$excerpt = trim(substr($excerpt, $len));
}
return $excerpt;
}
add_filter( 'get_the_excerpt', 'get_the_excerpt_filter' );
Hope this helps someone else.