wrap it in span and use internal style.
Note:internal style better than inline style.
.alert li a + span {
  display:none;
}
.alert li a + span {
  display:none;
}
<div class="alert alert-success dynamic-alert ">
    <ul>
        <li>
            (Canceled) <a href="http://www.google.ch">July 18, 2017 13:30</a> <span>Piano Lesson<span>
        </li>
    </ul>
</div>
 
 
you said : how could I move the content "(Canceled)" to the place of "Piano Lesson" and replace it? 
With jquery :
$(document).ready(function(){
  $('button').click(function(){
    var c = $($('li a')[0].previousSibling).text();
    $($('li a')[0].previousSibling).wrap('<span style="display:none"></style>');
    $($('li a')[0].nextSibling).wrap('<span style="display:none"></style>');
    $('li a').after('<span>' + c + '</span>')
  }) 
})
$(document).ready(function(){
  $('button').click(function(){
    var c = $($('li a')[0].previousSibling).text();
    $($('li a')[0].previousSibling).wrap('<span style="display:none"></style>');
    $($('li a')[0].nextSibling).wrap('<span style="display:none"></style>');
    $('li a').after('<span>' + c + '</span>')
  }) 
})
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<div class="alert alert-success dynamic-alert ">
    <ul>
        <li>
            (Canceled)<a href="http://www.google.ch">July 18, 2017 13:30</a>Piano Lesson
        </li>
    </ul>
    <button>Go</button>
</div>