Hi,
Well, you cannot delete posted budget. What you can do is to modify it (reduce).... Of course, it's better to pass this operation under separate document type, so it would be clear that it's just adjustment of remaining budget and not business operation.
Two more remarks:
a) If you have many lines with remaining budget, you can automate the process, but this would require a development
b) If you work with annual budget, then remaining budget shouldn't bother the user from functional point of view. Quite the opposite: it will show him how much he didn't consume.
Regards,
Eli