I'm assuming you're using jquery to slide the textbox up and down. Another method would be to toggle the disabled attribute of the textbox with jQuery when you slide it up or down. Disabled elements don't submit to the server.
edit:
I'd say right after or right before the code for sliding the textbox out, you'd do something like the following
<<when showing the textbox
$("#textbox-id").attr('disabled', false);
<<when hiding the textbox
$("#textbox-id").attr('disabled', true);
This disables the user from using that textbox in any way, including submitting it to the server, so the server won't see any values which might be in it.
edit2: Just remembered you'll also need to check the value of the checkbox when the form is submitted. If it's checked, check the textbox, if it isn't then don't.