"To challenge the petitions" means to question or dispute the validity or legality of the formal requests or documents that have been filed with an authority or court. Full definition
His two attempts to knock me off the ballot have failed — first by challenging my petition signatures, and second by challenging my residency. (newyork.cbslocal.com)
By challenging her petitions he can force her lean campaign to spend tens of thousands of dollars in legal fees to defend her access to the ballot. (citycouncilwatch.net)
Either side could request a hearing or challenge the petitions in court, he said. (syracuse.com)