Easy way to update a single translation entry without having to translate

Sure, the gettext filter does exactly what you require.

Here’s some code that should work out of the box:

function wpse31449_translate_my_stuff($translation, $text, $domain) {
    if ($text == 'Featured Image')
        return 'Post Image';
    return $translation;
}
add_filter( 'gettext', 'wpse31449_translate_my_stuff', null, 3 );

Note: if the translation is retrieved with a gettext context (_x() and _ex()) then the gettext_with_context filter has to be hooked to, which passes 4 arguments – the translation, the original string, the context and the domain to your filter.

Let me know if the answer is clear and/or how I can further improve it.