People convicted of certain crimes can’t circulate- ID theft, sex offenses, other fraud.
It is worth investigating under states' individual standards whether petitioners can be banned from circulating if they have certain criminal histories. In particular, sex offenses, identity theft, and fraud convictions are germane to whether a person should be permitted to gather voters' personal information. It is only possible to prevent these people from circulating if there is some form of registration in the state, so that officials are aware of who is petitioning. It would also need to be specified in state law that certain types of offenders are prohibited from gathering signatures. This provision could become controversial quickly and would require in-depth evaluation by each state about whether it would work. At the very least, make sure to fall back on establishing a system of registering each petitioner with the Secretary of State, and collecting the information necessary to run criminal background checks.