how to remove parent element if it exists?

Answer 1

Try this:

var paragraphsWithoutImages = $('p').not(':has(img)')

(Live example)

Answer 2

This will grab the paragraph not containing an image, which fits your limited sample:

var pt = $("p:not(:has(img))");

It's probably the case that your actual markup will be more complex than this but there are many variations on this that you could do.