Just the unconstitutional parts. And the text stays on the books, just with a citation to the court case that says they're unconstitutional.
When the courts strike down a law, they have an obligation to keep as much of it intact as possible.
Example: Affordable Care Act. The individual mandate was eliminated, but the marketplace, subsidies, medicaid expansion, and the preventive care stuff stayed in place.
It seems that an injunction with a token bond attached would still be enforceable under the proposed law.
There doesn't seem to be anything in the provision that requires the security bond to be substantial.