Theme:Twenty Fourteen, How to remove featured image on single post page for particular category

You can update the way image is displayed in template. in the page loop it will have something like this:

<?php the_post_thumbnail(); ?>

This grabs the featured image. You can wrap that in a conditional statement to check for whatever you like.

This would show it in every category apart from catgory 3.

<?php if ( !in_category( '3' ) ) : ?>

<?php the_post_thumbnail(); ?>

<?php endif; ?>

Further reading: https://codex.wordpress.org/The_Loop