So, how does this work? Does their legislature then have to reconvene and vote to remove it from the law books?
The legislature would not remove the laws even if/when SCOTUS finds them unconstitutional. The laws would simply be unenforced/unenforceable.
Lots of unconstitutional laws are still "on the books", but they're ignored by everyone including police, DAs, prosecutors, etc.
If you want an example: Lots of states had anti-abortion laws that became unenforceable when Roe v. Wade was decided. Some states even made new unenforceable laws. They sat there dormant until Dobs, then became enforceable laws again.