Looks like that link is part of an image MAP. There are three links there:
<img src="https://www.1stpetvet.com/wp-content/uploads/2014/01/usable.png" alt="facebook" usemap="#Map">
<map name="Map" id="Map">
<area shape="circle" coords="51,132,19" href="https://www.1stpetvet.com/blog/" />
<area shape="circle" coords="98,108,16" href="https://www.facebook.com/first24vet" />
<area shape="circle" coords="162,121,16" href="https://www.youtube.com/user/first24vet" />
</map>
So, whatever theme option or plugin was used to create this image MAP is where the link needs to be changed. I am guessing you took this site over? If no theme option or plugin was used to generate this then the previous developer may have created it outside WordPress and pasted the code directly into one of the theme’s files, such as header.php.
Given this line:
<link rel='stylesheet' id='twentytwelve-style-css' href='https://www.1stpetvet.com/wp-content/themes/twentytwelve-blank-childtheme/style.css?ver=4.4.4' type='text/css' media='all' />
You are using a Twenty Twelve child theme. I know for a fact that theme does not have image MAP creation built-in. The header.php should be in /wp-content/themes/twentytwelve-blank-childtheme/
Hope that helps.