It cannot be changed unilaterally. I'm sure all our friends in the un will allow us to change what we're not comfortable with. After all, the un and its members are our closest friends and they support us in all we do.
The discussion was about repealing the Treaty. There is always an out clause just as there is in the 1967 UN Outer Space Treaty. The Pres has authority to do this by himself and Congress has already given permission by adopting the Treaty and need not be consulted further.