I'd just beef up the server-side code so that it will ignore the parameter when the value is null, but if you insist on dealing with it client-side you can use DOM manipulation to remove the element from the page.
Using the 'display:none' CSS rule won't work since different browsers treat it differently (some will still submit the parameter, some won't).
Client-side manipulation is just too squirrelly for my tastes so I'll repeat my recommendation to deal with it server-side.
When I worked with IE4 a few years ago it didn't submit disabled fields. We had to write special JS to enable and re-disable read-only fields either side of the submit (using the readOnly property had other issues, in case you're wondering).
I dunno if that's still the case but it may be worth a shot.
Bear, I'm sort of stuck with this code as it is in a framework developed by another team. I am going to try to get them to change it, but I have to work around this problem in the meantime. So unless you know a way of changing the parameters in the request, I have to do this.
This is a hidden field, so it wouldn't be displayed anyway. I'll try the DOM idea and Jules' disable suggestion tomorrow.