There's no way to update an existing build without generating a new link.
"My Builds" section was added as a place where you can store build links (either for your own build or builds made by other people) with ability to search and filter the list.
If you need to make any changes to your build, you have to generate a new link, delete the old entry from your build list and add a new one, it's the only way to do that currently. This happens because build link points to a static data, which can't be altered, because it's shareable.
Theoretically in future I might add an option to save something like "drafts" for your builds in "My Builds" section, and you'll be able to update it as you please. But such builds can't be shareable (you can't generate a link for them) until they are made public. Otherwise this would lead to misunderstandings when you share your build link, someone bookmarks it, then you change it completely, and the person who saved the link opens it and doesn't understand what's going on.