Hide form if checkbox not checked

I have a checkout page with a default gift option. I have this code that allows to hide the gift option altogether:

<script>
$( document ).ready( function(){
$("#gift-form").remove()
});
</script>

What I'd like is for this code to not trigger if the page was accessed via the gift link. To my knowledge the gift link auto checks gift option checkbox for the user. Is this possible? Unfortunately I cannot edit the gift-form itself.

Thanks