Got the answer elsewhere.Will accept unless someone can think of something better.
This works perfectly using CSS (albeit adding content with the content: declaration) by drawing a triangle with borders instead of using an image for it.
CSS
.wpcf7-not-valid-tip {
background: red;
color: white;
padding: 10px;
width: 100px;
}
/* Updated code */
.wpcf7-not-valid-tip {
position: relative;
}
.wpcf7-not-valid-tip:after {
top: 100%;
border: solid transparent;
content: " ";
height: 0;
width: 0;
position: absolute;
pointer-events: none;
border-color: rgba(255, 0, 0, 0);
border-top-color: red;
border-width: 10px;
left: 50%;
margin-left: -10px;
}