You should remove the div that hold you link! There's no need to out the link in an div!
<div style="z-index:2;">link</div>
<a href="http://www.schedulicity.com/Scheduling/Default.aspx?business=AHDZC3" title="Online scheduling" target="_blank" style="z-index:3;position:absolute;">
See your working code on jsfiddle: http://jsfiddle.net/r4xeH/1/
Note: z-index only works on positioned elements (position:absolute, position:relative, or position:fixed)
Edit:
Updated the jsfiddle! Like I noticed, z-index only works if on positioned elements! You didn't position the <a href></a>
so the z-index never worked for the <a></a>
element and that's why the image was on top of the link.
If you look at your HTML, try to put styling in a CSS file, avoid inline styling. Also do not table's for layout. Tables must be used for showing data like you would in an Excel file. Use div's instead and position them!