Form AJAX - Update button value via Ajax
From the FAPI Reference:

#ajax['wrapper']
This property defines the HTML id attribute of an element on the page which will be replaced by the html returned by the #ajax['path'] or #ajax['callback'] function. Usually, a div element is used as the wrapper, as it provides the most flexibility for placement of elements before, after, or inside of its HTML tags. This property is required for using AJAX requests in on a form element.  Note that the entire element with this ID is replaced, not just the contents of the element.

So this:
'#prefix' =&gt; &quot;&lt;div class='mark-wrapper'&gt;&quot;,

Should be:
'#prefix' =&gt; &quot;&lt;div id='mark-wrapper'&gt;&quot;,

Also buttons don't have a #default_value, so replace:
'#default_value' =&gt; t($is_marked),

with:
'#value' =&gt; t('@value', array('@value' =&gt; $is_marked)),

And you should be on track (the change to t() is just for sanitisation, see Translating Variables).