I’m no expert but I think you need to stop the highlighting appearing when you mouseover the image.
Your CSS, creates a background colour when you rollover any link in the menu – this includes an image.
Plus the code for the link/image is all over the place.
<a href="https://www.vergeculture.com">
<img width="215" height="87" https://www.vergeculture.com/current=""
alt="Taste Magazine </a></li> <li>
<a href=" src="https://www.vergeculture.com/wp/wp-content/themes/Cutline 1.1/images/logo.gif"/>
current issue
</a>
There is an inside the <img> tag. It looks like you need to close the image tag first.
Hope that’s of some help.